If that is the case then they definitely need to clarify that clearly, as it stands no where under the Additional Equipment paragraphs is there any such restriction stated, and the bottom options make no differences of Wargear, Weapons or Armour (it pretty much just says “any 1 item of X availability“, baring GM Discretion of course).
A clarification might be in order indeed. However, you already noted yourself that getting guns, ammo and armour by that table becomes expensive.
I thought as much as well, if you have to actually purchase the ammunition separately this would effectively double to cost of the weapon in many cases which is neither fair nor friendly.
You assume that it's intended for PCs to be able to get hellguns on the cheap. Right now, your group wants storm trooper equipment without paying for it by taking the storm trooper specialization while the game intends you to either take the spec or be content with your t-shirt and flashlight. You can get a way out of that easily - just allow yourself some more points. You want a high-powered game, just ignore the 30 points equipment budget and replace it with something you consider appropriate. No problem at all. But such a unit is not a usual guard regiment, meaning it's not supported by the standard regiment creation rules.
In regards to the vehicles, if you look at the numbers it's not a problem. Sentinel Tactical Speed (so in combat) is 10m. Pretty much any PC (assuming at least 3 Ag Bonus) could easily keep up by running, and a relatively fast PC could almost keep up just by full-moving every turn (8m to 10m, for instance). So during narrative time, sure, there might be issues keeping up, but in combat (when it matters) it wouldn't be an issue.
I was referring to narrative time. To quote the regiment description:
Being used as the linchpin units in many grand strategies,
hunter-killer units use light vehicles with deceptively heavy
firepower to linger behind the front lines until called upon,
then pushing forward quickly to strike down priority targets
in support of the rank-and-file.
I would assume the pushing forward until you've reached the combat zone happens in narrative time. If you're a commander, which would you rather have when the Ork Waaaarghboss rears his ugly head? Four sentinels that can be at his location within fifteen minutes and hammer him with multilasers while supported by the line infantry or one sentinel and a few infantrists taking almost an hour to reach him and then probably only bring one multilaser and a heavy weapon to bear?
The gear sported by Hunter-Killers (not even long-barrel flashlights!) IMO indicates they're not intended to leave their vehicles, which only works if they all have a vehicle to not leave in the first place.
I do know that Sentinels do often work in packs, and it's possible to have a squad of Sentinels with no infantry support. However, I think what the Core Rulebook is assuming is that not all of the PCs are going to want to be mounted: someone might choose to play an Ogryn, or a Heavy Weapons Specialist, for instance, and probably didn't come into the campaign wanting to be in a vehicle the entire time, and likely doesn't have the stats to do so anyway. The rules as written allow for this, so whoever wanted to be an Operator or drive a vehicle has one available, while the rest of the PCs do their own thing.
If all your PCs actually want to do a vehicular campaign with no foot-slogging, then it's easy to just house-rule the issue and give everyone a Sentinel and then run a Vehicle-campaign. But I suspect that the number of gaming groups that want to do this is very small, so the current rules make more sense for the broader context.
The existence of Armoured Regiments (and their inclusion in the starting adventure) already proves FFG assumes some people want to go for vehicles only.
Additionally, there's already a regiment type for people wanting one Sentinel and some infantry: The Reconaissance Regiment. There, the infantrists are at least getting some gear of their own.
On the other hand side, there is currently no regiment for people that want more than one vehicle. So, talking about everyone being represented…
That being said, I've re-read the equipment descriptions and it appears you are correct in that every instance of an item being given to everyone says so. I think I'll open a thread about this issue somewhen later this day.