I have never been a mouthpiece "guy": my instructor told me to go out and buy a specific mouthpiece and that's what I used. When I started playing more jazz, I asked him what the best hard rubber jazz 'piece was and he made a recommendation, but I didn't exactly follow it . For a beginner, possibly the best thing to do is get a decent quality hard rubber mouthpiece. It's somewhat variable on whether the instructor will insist on the mouthpiece make/model, as mine did, so if he doesn't, here are a couple suggestions: 1. Stay away from metal or crystal mouthpieces. You will have difficulty controlling them and beginners shouldn't use them. (Sorry, Mr. Rousseau.) 2. Most plastic mouthpieces are very low quality. The major exceptions are the Yamaha 4C and 5C and the reason why these are exceptions is because they are extremely well made mouthpieces that are copies of older Vandoren designs -- but they're still plastic and don't respond quite as nice as a Vandoren. Almost, tho . * Possibly my favorite all-around mouthpiece has been the Selmer Soloist hard-rubber mouthpiece. This was recently re-introduced. Unfortunately, it's also close to $120 for the alto. The Selmer S80 is about $20 cheaper and is "decent enough", but a tad bright on some student horns. * I also fooled around with Vandoren mouthpieces for quite awhile. They are also very nice for playing just about any style of music and the V5 Classic is around $80. Not bad. * Also around $80 is the Meyer "classic" hard rubber mouthpiece. They're a little jazzier, but have a nice tone and are easy to control. * Around $60 are hard rubber mouthpieces by Bari. These used to be somewhat popular when I was in high school in the 1980's. I never played one, though. I don't like Runyon mouthpieces at all. There are a couple reasons: they're too jazzy and they're too gimmicky. However, I think every manufacturer can be rightly accused of being gimmicky at some time. (FWIW, I respect Mr. Runyon greatly and I even exchanged some e-mails with him before he died, but I just don't care for his mouthpieces.) Now, with most mouthpieces, you'll have questions about facings and tip openings and stuff. Just go for whatever's "medium". For what it's worth, I was a classical baritone sax player and I played baritone almost exclusively, even in lessons. I was taught by a second-generation student of Sigurd Rascher and then a first-generation student of Sigurd Rascher, so the mouthpiece I used was ... a Sigurd Rascher. Unless you're a glutton for punishment, are into playing classical music the way the German school does it or have decided to buy a 1940's vintage horn or earlier, in spite of what I've recommended, you don't want a Sigurd Rascher mouthpiece.