"Good for jazz" is a bit broad. If you are looking for a particular jazz sound - Hawkins? Getz? Brecker? Coltrane? Gordon? Bird? then you might choose a mouthpiece that suits. You also don't mention whether you play alto, tenor, baritone or soprano.
Anyway, a jazz sound is pretty much in your head. I can make a pretty jazzy sound on the stock mouthpiece that comes with any reputable sax. But my personal choice is a Claude Lakey which is a bit beyond your budget. You might pick up an Otto Link on eBay.
Unless your mouthpiece is absolute crap stay with what you're already using.
Drop your reed strength, and start playing with a "Jazz" attitude.
It's not the mouthpiece that dictates the style music you play.
I agree with Raphyel. A Meyer 7M is the only inexpensive mouthpiece I will use for jazz gigs. Although I prefer the more expensive Beechler and Jody Jazz mouthpieces, I've had many successful gigs on the Meyer.
+1 for Bandmommy's comments.
The Rico Graftonite (used to be called a Rico Royal Graftonite) is a very consistently excellent mpc for the money. I snapped up one out of curiosity when they first came out, the smallest one (!), the model A3, and it became my classical mpc of choice. Then, with a change of reed and ligature, that A3 opened right up and I played jazz quartet and lead alto in a big band on it for years, absolutely true. Attitude, developed chops, and some conception of what you want to hear coming from the horn make all the difference. Now I use a Phil-tone Meyer 6M, but I wouldn't hesitate to use my RR A3 in a pinch, or even the A5, A7, B5, or B7. The Brilhart Ebolin and the Runyon 22 are very viable choices if you want to step up a few dollars.
To the original poster: Listen to a lot of jazz alto, determine what sound you want to hear coming from your horn, and start striving for it. Some mouthpieces may help you lean towards your chosen sound more easily, but ultimately you will sound like you on any and every mouthpiece. Learning what you want to sound like is a majority part of the equation, and all that listening will also help your conception of jazz styling and phrasing. Whether you play your jazz on Selmer C* or D, a Rico (Royal) A3 or 5 or 7, a Ebolin 4 or 5, or a Runyon 22 is almost a minor detail; knowing your chosen mouthpiece's capabilities and your own capabilities are the true items you are seeking.
Lots of people here have huge mouthpiece collections (most of which sit unused in a drawer), and swear by their final mpc choice after years of hunting, so they will doubtlessly disagree with my statements here. Just don't let the mpc become your Holy Grail; develop your physical chops (embouchure, finger and articulation technique) and your mental chops (theoretical hearing of what you play against chord changes, and your mental concept of your desired sound and style).
Don't forget to have fun!
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