In World War Z, trying to treat zombies as a "military" threat is what got most of the army killed to begin with; so, if you're going down that rabbit-hole, you will want to reimagine everything about what it means to be an anti-zombie trooper vs regular infantry. Your ideas may be good for scouting areas that may or may not have zombies, but actually clearing a zombie infested zone would demand a very different military doctrine and equipment.
For starters, stopping a bite does not take heavy armor, but zombies can bite in a lot of different places; so, what you want more than anything is complete armor coverage. Instead of giving your zombie squads military grade body armor, give them something more akin to a shark bite suit. At only 18 pounds, you get 100% body protection for the same weight as most bullet proof vests (sans any ballistic plates). Even this may be overkill, but if your zombies have any inhuman biting strength (as they often do), a bite suit will break thier teeth before you have to worry about being bitten.
Now the armor will prevent a bite, but the shear size of a zombies hoard provides another threat which is often overlooked: crowd crush. If you organize your anti zombie teams like modern military squads where you spread out to prevent your whole team from being mowed down by gun fire, then your team members will be individually surrounded, trampled, and eventually ripped apart no matter how well you armor them. You can fix this by replacing 21st century military training with some late roman republic military training instead.
Modern riot control teams often study Roman maniple warfare because it solves many of the problems involved in how to prevent a large pushing force (like a greek phalanx, rioting protesters, or zombie hoard) from overwhelming and trampling a smaller maneuverable force.
I would also not give them same Enhanced Combat Helmets as the grunts. Romans used open faced helmets because it helped them see and coordinate better than the narrow openings of the older Corinthian style helmets and because they did not have any transparent materials that could actually stop the weapons of the day. Modern soldiers use open faced helmets for the same reasons. But modern riot teams use plexi-faced helmets. These give the same perception advantages as an open faced helm, but also protects the face from any bites, scratches, bludgeonings, and infectious spatering fluids from the zombies as well. If you opt for a single ubiquitous helmet, I'd chose one with a plexi face that regular soldiers may not need rather than one with an open face that would leave you zombie killers under protected.
Key aspects of this include:
- By giving your team riot shields (basically modernized scutums), you can create a flexible wall that makes it much harder for the zombies to pull your soldiers out of formation or tackle them to the ground. This is because your out-held arm acts as a shock absorber, and a shield is harder to get a solid grip on than an appendage.
- By standing shoulder to shoulder, you only need to fight one zombie at a time. If you have a shield, melee weapon, and armor, and they have thier teeth and fingernails, your odds of loosing such a 1-on-1 fight is next to nil.
- The person behind you can brace against you and help pick you up if you fall which will further prevent your formation from being overrun.
- By using short single handed weapons you are able to rotate out your front line as they get exhausted allowing them to catch thier breath and return to the fight later a full strength. While a pike wall, or riffle teams with long bayonets may work great on the short term against zombies, they make rotating out your front-line impossible because you have to break formation by lifting all your weapons to let your own people through; so, if you are too outnumbered your front-line will be forced to fight until exhausted at which point they will be easy pickings. Short weapons also makes it much easier to reorganize your battle formation if you need to expand or contract to fill a gap, or move through complex urban environments. They also pair better with shields than longer weapons because your shield can hold your enemy where you need them for a shorter more accurate weapon to find its mark.
- You can open and close gaps in your formations intentionally to allow small numbers of enemies into your back lines where you can surround and more easily kill them. This will be particularly important if your setting includes any "super zombies" that might otherwise trample right through your lines like a war elephant.
- Bullets not required. While arming your troops with guns will be a good way to safely kill small amounts of zombies at a distance. Zombie hoards can be huge, and there is no guarantee you will have enough bullets to finish the job. A maniple is organized to be able to fight for hours on end without breaking; so, if you run out of bullets, you can just keep knocking skulls in until the job is done.
A modern riot team of a few hundred men using such tactics can control tens of thousands of rioters without taking any significant injuries, and they are not even allowed to kill the rioters. So, controlling a zombie hoard with lethal force is going to be overwhelmingly effective.
As for weapons:
While the Romans preferred the Gladius for its ability to thrust at gaps in the enemy's armor, they were not ideal for penetrating skulls. For zombies you will specifically want a more front heavy weapon. A warpick, hatchet, or hammer would do a good job, but the ideal weapon may actually be a khopesh. The khopesh has the weight profile of an axe making it good for penetrating the skull, but the extended cutting surface means it would also be really good at lopping off zombie hands that try to pull your shield away.
For your firearms, low calibre handguns allow the most ammo for their weight and cost. Since zombies don't have guns, you don't need to engage from really far away to have the reach advantage; so, high powered rifles are a bit wasteful. Instead you wait till you can "see the whites of thier eyes", and go for headshots. The pile of bodies from the zombie's front line will create a barrier; so, as long as you have a solid firing line, you can hold the whole hoard at bay at relatively close range meaning you don't need more than handguns. To this end I suggest any plain 9mm police issue sidearm with a lot of spare clips. An M16 with 45 rounds has about the same weight and cost as glock 22 with 120 rounds of ammo.
Modern police are trained on and issued a wide array of weapons and defensive gear, and only bring what they need based on the threat. Likewise, your anti-zombie legions may have M16s they are trained on for fighting off human raiders, but if they are being deployed to fight zombies, they will leave the rifles at home and bring the right tools for job, just like cops don't bring thier assalt riffles to a riot.