WHATS A GOOD SIZED MOUTH PIECE TO USE

do you have a large bore horn or what?

If you just began playing the trombone, the standard mouthpiece size is a 12C. If you're looking to get a better tone, I would suggest a 6 1/2AL. Your high range will suffer a little (which will come with time), but you will get a much better sound. I hope this helps.

"small", tenor horn-if you've played a while, 6-1/2AL. If you have a large-bore horn (mine's a .547) 6-1/2 will do, but my new fave is the 5G. Same rim, but deeper, and the apertures are larger too. Great for good column support, and you can get way down, and then way up in the register too.

Actually, a 5G is larger in rim size than a 6½AL.

As for the original question, there is no correct or incorrect answer.

It all depends on your lips' morphology, what sound you want to get, what horn you are using and what style of music you are using it for.

In general, classical players use large bore instruments. They usually play on a mouthpiece sized between 4G/4AL and 6½AL (approx. 52 to 48 in Schilke/Yamaha measurements). Some use larger stuff (3G). Bass players will usually go with 1-1,5G, with some playing on 0 or 0,5. Then again, it's only *in general*.
For example, in France, almost every tenor players use 6½AL, and bass players rarely use bigger than size 3-4 (which are tenor pieces in N. America!)

Again in general, jazz players play on small bore instruments (though one of the top jazz players here plays on a Bach 42!). And they usually go with smaller mouthpieces. 11C (or equivalent) is a very popular choice, as well as 12C.
I personnally use a Yamaha 48 with my Conn 12H because the difference in rim diameter between my large bore/classical piece (Yamaha Alain Trudel and now Ferguson 1) and my jazz piece would be too big if I played on something smaller.
I keep the 12C for alto playing.