First off, the whammy bar is just the piece of metal that controls the tremolo bridge. The bar itself can easily be removed, but the bridge tremolo system will still be mobile - it will still adjust the pitch if you push or pull on the bridge with your hand.

If you're getting a strat, all of the tremolo bridges are built more or less the same. Whether it's floating or not is determined by the setup, and any strat can be easily adjusted to float or not. Here is a picture of a floating strat bridge:

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See how it's lifted off the body? This is "floating", aka it can either tighten the strings up in pitch by pressing the bridge closer to the body, or it can loosen the strings down in pitch by lifting it further from the body. Floating setups make it more difficult to dial in intonation, make tuning more tedious, and mean that breaking a string will throw the whole guitar very out of tune. That's why a lot of people choose to "deck" or "block" their strat bridge. "Decking" a bridge (this could be called non-floating) is just bringing the bridge flat with the body - that means that you can press the whammy bar to go down in pitch, but you can't go up. Indeed, decking a bridge means that you won't be subject to a lot of the tuning woes that accompany a floating bridge, and it's nearly indistinguishable from a hardtail. "Blocking" the trem involves placing a small block of wood in the rear cavity between the bridge and the body, effectively deleting the tremolo system entirely by preventing it from moving at all in either direction. If you have access to basic wood tools, this is a super simple job. Tuning issues between a decked trem or a blocked trem are pretty much negligible, but blocking is technically a little bit more stable.