do all of these shoot 223's or are their different options?
which caliber is the best and cheapest?
There are a few calibers available, but 5.56/.223 is by far the cheapest. Buying military surplus ammo is as close to cheap as you can get.
"Best and cheapest" don't really go together in my opinion. It all depends on what you plan to use it for. If you want to deer hunt with it, I would suggest 6.8 SPC or 6.5 Grendel, but the ammo is also really pricey.
That PSA up there^^^ is one hell of a deal. If you want a good starter, that's it.
Most people build their own lowers and buy an assembled upper. It isn't necessarily cheaper, but it's cheaper in the sense that you get everything exactly how you want without wasting the factory parts.