Bulk Freighters will be Ovoid shaped.
When it comes to optimizing structural integrity with air resistance, the best shape is an ovoid (egg shaped). The forces involved in atmospheric acceleration and re-entry are significant, and the larger and heavier you get, the more integrity becomes the biggest issue you face. Making a long skinny rocket shaped ship will suffer more crush force over its smaller cross section as you get too big, a perfect sphere would have too much drag, and anything with sharp corners like a cube is less structurally sound under the heat and stress. Wings are especially fragile as you scale up in size and speed; so, while space planes are great for smaller loads (100 tons or so), they would be terrible for larger ships.
In real life, goods are typically transported either via bulk carrier for transporting massive volumes of unpackaged products or container ships for when you have lots of smaller parcels to deliver and distribute like consumer goods. Ovoids will of course be perfect for bulk carriers since things like grain, water, ore, fuel, etc. don't really care what shape they are in, but container ships will require a bit of extra engineering.
Shipping containers are cuboid for many reasons. They are ideal for putting smaller boxes into, they make good use of the space, and they are able to be directly loaded onto trucks for transporting the maximum amount of goods for distribution. So it is best not to mess with the cuboid shape of a shipping container, but it does lead to concerns about how tightly you can pack your cargo in a spheroid. For it's length, width, and height a spheroid has ~47.6% less internal volume than a cuboid. So, while cubes can't survive high delta-Vs or air breaking nearly as well as a sphere can, they may still be the ideal solution.
High Efficiency Fusion engines are crazy cheap to operate compared to traditional rockets, and are basically immune to the tyranny of rockets problem. Assuming Perfect Efficiency, each ton of cargo fired at traditional Delta-V only requires about 2 grams of hydrogen fuel. Let's say we consider "High Efficiency" to mean some fraction of perfect. Now we need to make up some exact number for what "High Efficiency" means... but I think most people will interpret this to mean some tangibly large fraction of the total energy. Conventional Rockets are about 70% efficient; so, let's go with that and say you need about 3g of fuel per ton. This means that the fuel cost per ton of launch weight is about /$0.003/ton if you are using hydrogen fuel. While some of you might be thinking that fusion will require much more expensive deuterium, tritium, or He3, current research into fusion technology predicts that heavy versions of hydrogen can be created as part of the nuclear process before we reach economic viability, much less high efficiency. So, plain old hydrogen is the most likely fuel source at this tech level.
The reason this is all so important is that it means you don't need over 4G of acceleration to get to space on a budget. A cuboid container ship will need to burn a lot more fuel and move a lot more slowly than an aerodynamic round ship, of similar mass, but the cost of getting to space will still be super cheap. Even if you burn 10x as much fuel going up at a modest 0.5G all the way. That still places your at only 3 cents per ton in fuel costs... now the extra weir and tear on your thrusters will likely be a lot more expensive than that, but the extra efficiency of stackable containers should still out weigh this fact.
For structural reasons, you will still want your ship to have a rounded bottom (plus you want them to be able to use the same ports as bulk carriers); so, the whole bottom will be the same as the other ships, but the top section can just be shipping containers bolter together in a more or less cylindrical pattern.
More cubic shaped designs will be oncourse be viable for smaller container ships.
Space Port Design
Space port design will work more or less like a normal modern rocket pad. But because you have "incredibly efficient catalyzed direct fusion drives", you can handle WAY bigger payloads using the same space port technology. The largest rockets used today weigh about 4000 tons with a 150 ton lift capacity, but with direct fusion drives your fuel efficiency is about 500,000 times better than Rocket fuel; so, a 4000 ton ship needs only needs about 11.4 to 100ish kg of fuel to reach orbit depending on if you are trying to maximize your delta-V or just make it as smooth of a ride as possible.
Furthermore, traditional rockets have a much smaller base section than these ships meaning that issues like distance to landing struts, sonic and thermal kick-back etc will be more spread out and less of a problem. In fact, height, and not total size is a much better gauge of how hard it is to make an appropriate launch platform; so, using the squattier designs like the ones shown above could easily be 10x the mass of a Saturn V Rocket, and not require any additional technology to make an appropriate launch-pad for. You just need to make it wider.
Furthermore you can overcome many of the things that make normal VLS rockets difficult. In a normal space rocket, your goal is to accelerate as fast as possible with as little complexity as possible because the more time you spend getting off the ground, the more total Gravity you have to overcome. This is especially complicated at take-off because that means your first stage rocket gets a lot of kickback both in terms of heat and sonic reflection. We currently solve for this by shooting up jets of water at the thruster as it takes off which absorbs the heat, boils, and then the bubbles absorb the sonic feedback. The other thing we do is limit initial takeoff accelerations to about 5m/s^2 (which is much lower acceleration than once it gets away from the pad). However, in a ship where fuel is less of an issue, you could limit takeoff acceleration to much slower (1m/s^2) reducing actual downward thrust and kickback at launch and landing time at the cost of using a bit more fuel. This means that you could go an additional 50% bigger (in all directions) and modern space pad technology would still get the job done.
This places the maximum mass of a heavy freighter somewhere in the 135,000 ton category when fully loaded... though I suspect something in the 40,000 ton weight class may be more common since throughout most of civilization, the majority of cargo ships seem to be about 1/3rd the mass of "top-end" ships because it makes building to tolerances much easier. Given this size, economy of scale, and figures taken from various sources, I'd estimate this as being 15-30% ship/fuel, and the remainder of the mass as cargo.
As for how expensive these space ports are... they are not really more expensive than a normal airport. Yes you need a large exclusion zone because of the power of the thrusters being so loud and hot, but because it is a VTOL design, you don't need long paved runways; so, a fairly small total facility in the middle of the desert or a small rocky peninsula would suffice.
That said, smaller versions of this design would not need specialized launch pads at all. 50 ton ICMBs can be launched directly from the back of a truck in the middle of a normal road; so, smaller ships with this wider profile (500 tons, maybe even bigger) could still be launched and landed safely from open fields or simple paved surfaces just like these 50 ton missiles. In all reality, your fusion engines should mostly make space planes obsolete since anything too big to VTOL will also be too big for wings. The biggest application I see for space planes will be where sustained in-atmosphere maneuverability and speed will be important or if fusions reactors simply need to be to big to work with smaller ships, and you need good old fashion chemical propulsion for smaller crafts... so, you'd probably still see them used for military purposes where you need aircraft that can perform both air and space missions and/or for non-bulk purposes.
Do you really need ships that can carry 100,000 tons?
... the transported cargo (up to space) would mostly be small, extremely refined goods like microprocessors, cryogenically-packed fruit and vegetables, and other goods only unique to earth. The vast majority of freight stays orbital, or dropped down the gravity well on single-use, dirt-cheap reentry capsules.
Because you have such cheap fuel, it is actually better to not do this. Fusion engines and reactors are very expensive and hard to make... but a few kg of hydrogen is very cheap. In fact the total fuel cost of launching 100,000 tons of cargo into space would be between about /$400-4000 in today's economy. In terms of shipping, that is dirt cheap. You could potentially run hundreds of missions with a reusable heavy freighter for less cost than it would take to build 1 single use rig.
This means that you want to have a 2-way freighter designed to go both ways and be reused over and over again. This is very different then modern rockets where the fuel is really expensive and the rocket is by comparison cheap. Even if your return trip back to space is only carrying a few tons of processed good, for every 100,000 tons you are bringing down here, it's still worth it. Being able to send your fusion engine assembly back up into orbit is already a necessary cost, so might as well use the ships you've already got... not to mention, manufacturing and refining on Earth will be much cheaper; so, most if not all ships, ship parts, and fuel production will need to be done planet side anyway.