Re: Trem questions.
Floating means that the bottom of the bridge does not rest on the body of the guitar. Instead, it's raised up a little bit, and it's set up so that it is parallel to the guitar body. You adjust the spring tension so that it fully counterbalances the string tension. Floating trems allow you to pull up and push down on the bar, whereas a trem set up flat against the body can only be pushed down.
The disadvantage to floating trems is that they can be trickier to set up, they don't sustain quite as well, and some people feel they give the guitar a thinner, less full sound.
As for the difference in trems, the Bigsby is meant for subtle vibrato work, they generally don't hold their tuning as well as other trems. The Fender tremolo is a much more compact unit than the Bigsby, and they generally stay in tune better when set up well. They have a very smooth feel to them, which is why some people prefer them over Floyds and Bigsby's. The Floyd is the ultimate trem for people who love to do whammy bar tricks. The strings are locked at the bridge, and then a set of locking blocks is clamped down over the strings at the nut. Because the strings are locked at both places, guitars with Floyds will stay in tune better than any other guitar when set up properly. The downside to Floyds is that they feel differently than Fender trems, and they're geared more towards extreme whammy bar tricks than subtle vibrato. They are not difficult to tune or set up if you know what you're doing, although they do take a bit longer to change strings on than other guitars. Floating Floyds are generally the hardest to work with, but it's no big deal if you learn to set them up properly.
I highly recommend Dan Erlewine's book "How To Make Your Electric Guitar Play Great." Read it, then read it again, then you can begin working on your own guitars. Much more rewarding to do the work yourself, not to mention cheaper, and you can make sure it gets done right the first time.
Ryan