OK, apologies for the slight delay caused by visit to dentist...... Deep Joy!!
Right, for these purposes, let's say that there are basically 3 Popular Styles of Trem.
The vintage 6 Screw Style. Commonly found on older models and reissues of same from the Fender Strat Family.
So called because of the 6 screws that hold it on to the Body of the guitar.
The 2 Post Style. Again, can be found on various Strat style Guitars and is popular with other makers as well.
Basically, where on the vintage style trem you have the 6 Screws, with this style you have 2 Posts on which the leading edge of the Trem Plate rests. Many people prefer this system as it can lend itself to some serious whammy action and "can" hold its tuning rather better.
The Floyd Rose Locking style Trem. This is the "go to' device with players such as Satch, Vai, etc. This is a Fully Locking System that basically allows you to be a complete hooligan and have the strings hanging off the fretboard, then return to pitch without any major issues.
What needs to be addressed from the outset is that any
trem can be made into quite a versatile tool provided it is set up correctly and I am talking about many factors here, The Nut must
be cut correctly so that there is no binding when the string moves.
The Machine heads and string windings. Ideally, try and find a guitar that has some form of Locking Tuners, this really does help with Tuning stability, whilst not essential, they really do help, so if the guitar has them already fitted, BONUS!
String winds on the Capstan also play their part, always make sure that you have enough winds and that they are neat and tidy, NOT looking like a Ball of wool!!
Lubrication. Yes, it is a guitar forum, you haven't stepped into a parallel universe
. Lubricate the nut with some graphite paste, or rub the slots with a Pencil Lead, but the best stuff I have ever found is a lubricant that the Radio Control Car builders use for their Diffs, pop into a decent Model shop and they will sort you out.
Springs and Numbers of same.
The three Trems mentioned all rely upon Tensioned Springs which are found under the backplate of most guitars.
You can alter the tension of the whole assembly, by choosing the correct amount of springs and how they are spaced.
What do I mean?
OK, I like my Trems to be floating, which means that you can dip a note by pushing down on the Bar, OR, raise the note by pulling up. I use 9 Gauge strings because I am an old fart with arthritic fingers, the set up that works well for me, is to have 2 Springs fitted, on the Block of the Trem, I use the outer holes and on the Spring Claw I have the other ends on the centre two prongs. I like a light and responsive trem action and find that the angled springs produce the right amount of pressure. You could use 3 Springs straight, but I find that this gives just a bit too much resistance where the two angled works perfectly for what I personally want.
I have both the 6 screw style bridge and the 2 Post style and for what I do, the 2 Post is my favourite, that said, my 6 screw one works almost as well, unless I get heavy handed, at which point the tuning "can" suffer. The 2 Post seems absolutely Rock Solid.
Floyd Roses etc. Now these are considered to be the ultimate trem if you really want to get int the Eddie Van Halen styles. The are a fully locking trem which means that instead of a conventional Nut, you have a Locking one which Clamps the strings in place. You have Fine Tuners down on the tail end of the Trem for...... Fine Tuning.
The disadvantage to this style is that for the inexperienced player, they can be a complete nightmare to set up if anything goes wrong, and restringing takes on a completely different perspective. LOL
However, PANIC NOT!
We can get you through all of this without too many problems.
Along with Daniel's excellent suggestion, I would add this. Buy "Tremolo Bar Techniques" by Michael Casswell on Lick Library, it is the best education you will EVER get for setting up and using a Trem. I regard this as vital watching now and cannot recommend it enough.
Phew.... Coffee and Painkillers please.