There are some basic (and obvious) guidelines I can offer: if you want a dark, 'Classical' sound, use a more closed tip with a heavy reed, like a Vandoren M13 with a #4. If you want a brighter, more flexible sound, suitable for jazz or Klezmer, try a Bernard Portnoy 03 with a 2.5 Alexander, etc. The only problem with this is that there are a zillion mouthpieces out there and way too many brands of reeds!
Not only will you have to crack open that piggy bank til it hurts but, as many folks don't seem to realize, your embouchure changes with every mouthpiece change you make. For the first couple days, all you notice is the difference: "Wow, what tone/high range/flexibility", you think. Then, a strange thing happens - you start to sound less like the mouthpiece and more like yourself! Your embouchure is adapting to the change and you are starting to slide back into the problems/habits that made you look for a new mouthpiece in the first place.
So, if you possess a good instrument in good repair and you already practice regularly but are dissatisfied with your sound and want to make a change, try this: buy a bunch of the Rico Royal Graftonite mouthpieces and be scientific about it - they only cost about $16 each on Amazon, so you won't go broke. The 'A' has a large chamber for a darker tone, the 'B' a medium chamber for a more middle of the road tone, and the 'C' has a smaller chamber for a brighter sound. They also have 3 tips: the 3 (more closed facing with a shorter lay), the 5 (medium facing and medium lay) and the 7 (open facing with a longer lay).
I'd stick with the A and B, unless you really covet a bright sound. Try the different facings with a good, middle of the road reed, like a #3 VanDoren bluebox, and see what you like, playing each for at least a few days so you can distinguish between the sound of the mouthpiece and your sound WITH the mouthpiece. You might be pretty well satisfied with a Rico, as they are well designed and material doesn't matter much as people would like you to believe.
On the other hand, you could take note of the measurements and look for a 'better' hard rubber mouthpiece of similar playing characteristics. Selmer, Vandoren, Portnoy, Hawkins, and many more are excellent pieces. Myself, I use a Rico B7 with a Fibracell reed (I know, I can hear the classical players out there shuddering). I get a sound that I like and the reeds require no soaking, scraping or other maintenance.
So, next time I'll talk about reeds....