Warfare is hell.
The first step would be to set up a defensive perimeter. It would take an engineer company (for example the 397th Engineer Battalion) with some horse-drawn carts for daily supplies (we requisition that from the ally) and tools (shovels, axes, chainsaws, fuel), several carts for gravel (requisitioned locally), steel rebar (import, takes some of our space), wood planks (requisitioned locally), rocks (requisitioned locally) and hard work as fuel supply and weight limits in the supply route are low. But it will work.
The Engineering company of 50 is grouped in 5 groups. Everybody is armed with automatic rifles (M16, AR18, G36) and has about 2 boxes of ammo (typical packing: 800-1000 per can) in their deployment kit. One in 10 has an 40mm grenade launcher like the M203, one gets a DMR. Everybody gets a combat knife. Spade, pickaxe, cutters and machete complete the armory.
Within just some week or two they will errect a modern version of the Maginot line over a sizeable stretch. To this, they also build gravel access roads.
The Engineer company subsequently moves on to extend the line to defend the docking/landing area stockpiles supplies. Each trip a ship comes in, it also should drop of parts for construction as well as fuel barrels. Diesel for construction equipment, gas for the chainsaws and Kerosene for later use. It doesn't even have to be much: each shipment just brings in a pair of barrels instead of 2 men, so it will stockpile over time.
2nd Wave: Mountaineers
Meanwhile an infantry batallion or two (ca 50-100 men) move into the fortified positions and mans the fortifications. It might be better to send units like Mountaineers, that are better trained and have heavier equipment. I think the Bataillon médian de chasseurs ardennais might be an excellent choice to use a template for such a unit, but that's just because I love the fact 40 of them held up Rommel and his 7th Panzer Division for 18 days until they ran out of ammunition.
Armed with "light" 60 mm mortars, squad machine guns, possibly a heavy machine gun, some DMRs and everyone else with automatic rifles, they can hold this position as long as ammunition is there, which could be pretty much indefinitly (as elaborated here) as supply caravans roll in and increase the stockpile over time. No sane military would send a crew of soldiers into an area where they can't supply them. Or at least none that learned from WW2. Since roman times, human warfare always was around logistics constraints and WW1 and WW2 did teach a lot about how to keep logistics flowing in the worst situations.
Besides the 60 mm mortars, they also might bring light field artillery, which can be drawn by horses. 7.5 cm Pak 40 fits this bill and weight about a ton and a half. If 60 mm artillery isn't enough, one might go for 100 or 120 mm mortars, on the cost of ammunition capacity, but it would turn any 12th century fortification into a shattered field. If the PAK 40 is too heavy, short-barrel variants might be a better fit - and some of these might even be disassembled for transport. For example the 75 mm light infantry gun the germans used in WW2 had variants that could be turned into packages and weighed only about 375-400 kg for 3500-5100 meters range.
For mowing down infantry, quad-mounted machineguns like the M45 Quadmount or the infamous Flakvierling could be drawn by horse and haul their complement of ammo - and only weigh 1 or 1.5 tons each, making them equivalent in deck space to a 75 mm field artillery.
As an alternate to regulars, sending in irregular troups might be an option. Irregular units means troops that are not national military. Guerillia Warfare is the modus operandi of such irregulars - and La Resistance was a particular large and well organized group of Guerillia during some parts of WW2 (mainly during the German occupation and before D-Day).
Think Ernesto Che Guevarra. In 1956 he had ca. 20 men left of the original 82 after the landing in Cuba from the Yacht Granma. They connected with local guerillia networks to arm up, resupply and reinforce. Their most vital supply item was ammunition - food they sourced from the locals for help. They turned locals into Guerillios (which loosely traslates into 'fighter' or 'warrior'). At the time of the Battle of Yaguajay two years aftet the Granma landing, Che and Castro had more than 450-500 men and a tank.
Armed with every gun they can get their fingers on, there is no standard equipment in the Guerillia troops. They fight with what they can get their hands on, but they strive to standardize on one type of ammunition if possible. In the case of the IRA it was during the riots a mix of AR-16, M16 and AR-18s, relatively standarized. They also pack lightly: drawn out fights are a bane. Instead Ambush, Assasination and blowing up supply convoys are often preferable to 'honorable' battlefield fighting. They blend in with the surroundings, try to wear the clothes of the people that live there and work with the sympathies. Mao Zedong did summarize Guerillia Warfare like this:
The enemy advances, we retreat; the enemy camps, we harass; the enemy tires, we attack; the enemy retreats, we pursue.
To accomodate our need for logistic backup, Fantasy-World will have to run a massive expansion on shipbuilding, aided by modern engineers from our side that helps in streamlining the making of the hulls as quickly as possible. Gone is the wooden keel and replaced with a steel frame, to which the planks are riveted. Silicone for sealing instead of horse-hair and tar. Each ship that returns could bring another frame that was preconstructed without taking deck space from on our side (put it over the ship like a tent) so the longships could multiply like flies.
Engineering crews could probably easily refit the longships with small fuel driven motors and reinforce the hulls to allow heavier transport to get them to an average speed of 6 knots and independance of wind and thus massively streamlining the delivery times, though not necessarily cut them down.
Reinforced hulls would also allow the transportation of Jeeps and light trucks and larger field artillery in addition to motorcycles and light infantry guns, which were possible before. No tanks, but still, Motorisation makes the warfare much more mobile!
Our modern logistics meanwhile would work as much as they can on speeding up the loading of the longships on our side. For example we could skip the trip from wherever the portal is to our shores. No matter where the portal is, tender vessels can wait in the area and stock the longboatd out there on the open sea.
Our reinforced boats also are probably might be just big enough to transport heavier engineering equipment - even if it has to be taken apart. Think Jeeps with a plow or an excavator on the back. Once the first excavator is on the other side, we can extend the trenches much faster. The bulldozer and gets assigned to building supply roads and clearing an airstrip together with the engineers. Note that we might want to shift to shipping more fuel and ammo at that point, entire shiploads of these supplies in addition to reinforcements.
Once we established our frontline - which pretty much can be held forever, time is no longer of an essence. Supplies will accumulate in the landing zone as transport volume (hopefully) increases. It doesn't matter that ships take weeks, if you just have enough ships.
Taken to the Air.
The Kerosene is for simple biplanes, which are light and easy to be taken apart for transport, or even better, folding-wing planes. Most don't actually need a landing strip, they could land on any field that is flat and large enough, though an airstrip is clearly preferable. For a squad of 3 planes, we'd need 6 pilots, about 4 ground crew and an engineering crew of about 5. Their tools and equipment including the planes (with detatched wings) can be transported via carts, and most turboprop planes are extremely reliable, making the need for replacement parts somewhat small.
They serve as spotting and CAS planes. They push the perimeter from about 3 kilometers to a couple hundred kilometers kilometers, which in combination with radio technology, would allow much more targeted defense or offense along the perimeter as well as stratetgically destroying supply trains. They might need to be used sparingly due to fuel constraints, but their intimidation factor and attack tange could turn the tide in some battles.
Onto the attack
While our troops don't get to become mechanized troops in APCs, the increase of transport volume for fuel and the presence of light trucks - think Opel Blitz - and towed light artillery and light anti tank guns has turned our battalions into motorized troops, which are much faster in deployment. Once enough fuel has accumulated, the battalions roll out in a Blitz with CAS-support, then the gained lands are fortified. This is repeated till the evil army surrenders or is turned into a stinking pile.
If the Blitz isn't showing enough results, our military also might ship over some light missile artillery to aid in the attack. Katyusha for example would stretch the attack range of our assault force to 5500 meters, devastating an army that can't even see our advancing troops and turning a medieval city of the opposing forces into a field of rubble.
The City-Killer Batallion
Or, we could just send a single shipment. A single shipment of 10 M29 recoilless rifles, 30 men with Armalites, a box of ammo per man. And 10 Mk-54 Davy Crockets. Once in Fantasy world they requisition some horsecarts, stuff them with materials and food and embark into the enemy lands. It's a small caravan, they will use side roads if possible and try to evade any enemy contact, killing whatever they encounter. Tehy march until they get close enough to the first enemy administration center or military gatehring zone. There 3 disembark with one recoilless rifle, a Davy Crocket and the rest circumnavigates the place, marching on to the next target, possibly leaving the carts behind as they distribute and go into their respective positions. Then... A single Radio call and....
BOOM. The first target is turned into nuclear wasteland. Only then we send our demand: Total surrender within 24 hours, or the next place will be annihilated - we don't tell them which. No answer? Laughing? BOOM! Still no surrender? BOOM! We can go on... they don't know how many we sent. They only see that not surrendering immediately results in cities turning blazing ashes.
We can take this even to the next level: Not 3 men per nuclear explosion, 1. We modify Davy Crockets to detonate on a trigger signal instead of on impact. Then, we gold-plate and decorate the housings and send them as Tribute to the enemy administraors we can reach with one of our own spies to 'gift' it to the governers in exchange for a ceasefire or release of captured troops. Once they reach the target, we simply state the conditions for their surrender, and if they decline, we blow up the whole town.
Then we send a new ultimatum to the next we can reach, together with another agent armed with a bomb. But our terms are different now: Total, unconditional surrender or total annihilation.