If you're like me and don't have the big bucks to shell out for a professional horn, you can get a lot of mileage from a mouthpiece upgrade.

Biggest factors in the sound of a mouthpiece are the facing and the chamber.  A closed facing will likely give you sharp notes in the upper register.  A more open facing will allow you a more prounounced vibrato and more in tune upper register.  When you open up the facing however, you'll need to compensate with a softer reed as you get more open.  As far as chamber, a more cavernous chamber will give you a darker sound (more suited for concert work) and a chamber that more tapers into the neck opening will give you a brighter tone and more projection (louder).  Metal mouthpieces also give you a ton more projection, so they aren't going to work as well for you if you have to do some quiet classical pieces.

Beginner mouthpieces are fairly closed facings (Selmer C, C*).  You probably want to open that up some.  From a beginner facing, you could probably go to a C** or D in the Selmer mouthpieces without changing reed strength.  You'll be able to get a deeper vibrato and I've found a lot more stability in the altissimo register with more open facing mouthpieces.  You can find a chart, probably somewhere in these forums, that compares the facings for all sorts of mouthpieces of various brands.

I currently play a Selmer Short Shank Soloist D.  It seems to sound pretty good in just about all playing situations from classical to rock.  It will probably be just a bit over $150, but I like the way mine sounds.

Search through the forum for tips from other folks.  I'm almost 100% certain that you're not the first to ask this question.  Good luck to you.

Hi Tori, Since you're playing on Java #4s it sounds like you've got some chops developed and could truly benefit from a good mouthpiece. For the versatility you desire, it seems that a good hard rubber piece with a large chamber and low baffle, of the general type described by mikey, would be a good choice. Meyer and Otto Link pieces have a somewhat larger chamber than the Selmers, adding some depth to the sound. You'd probably do well with an intermediate tip opening, about .090 to .100, for good dynamic control and flexibility of tone. Under the Link system that would be a 6, 6*, or 7. Larger openings will result in a darker tone unless you want to play louder. When you get your new piece, by all means try out some different reeds to see what suits you best.