You should, of course, read
http://www.woodwindforum.com/forum/showthread.php?t=2547.
While there are a lot of cheap clarinets on the market, there is no guarantee that cheap = good.
As an introduction, modern clarinets are made of wood (a few different kinds), plastic or metal. The metal horns that are currently available are either expensive professional horns or really low quality instruments, with no in-between. Avoid these. Plastic clarinets are your standard cheap student horns: we'll get to those in a few seconds. Wood is generally reserved for intermediate and professional clarinets.
Additionally, you want a Bb clarinet. There are approximately a dozen other members of the clarinet family.
But we're talking inexpensive beginner horns.
First, it's very hard to go wrong with Yamaha. A new YCL (stands for "Yamaha Clarinet")-250 sells for around $700 US. However, you can sometimes get older, warrantied and overhauled Yamaha student clarinets for under $250 (again, see
http://www.woodwindforum.com/forum/showthread.php?t=2547 for some ideas of where to buy an overhauled, warrantied horn).
Let's simplify the Yamaha model names, though. First, remember that it'll be in the form of "YCL" for "Yamaha Clarinet" and then a number. Here's what those numbers mean:
2x or 2xx: Plastic student horn, where "x" is any number.
3x (generally 32 or 34): Wooden intermediate model.
450: Wooden intermediate model; replacement for the YCL-32.
6x or 6xx: Wooden standard professional models.
7x or 7xx: Wooden custom professional models.
CSx or CSxx: Wooden custom-built professional models, where "x" is any letter.
SEx or SExx: Wooden custom-built professional models, where "x" is any letter.
The idea is that if you walk into a store to buy a Yamaha clarinet and have a choice between, say, a YCL-20 and a YCL-34 and the 34 is slightly more expensive, get the 34: it's a better horn.
Again, if you're going to buy used, you want to get a recent clarinet that is fully overhauled and preferably with a warranty. If you're getting a wooden clarinet, if the ad says that it has cracks or pins, or has been cracked and repaired, SKIP IT.
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Buffet also makes some really decent student clarinets. The Buffet B12 (NOT the B10) is a fairly decent horn that has been described as a plastic version of Buffet's flagship R13 professional horn. Yes, they're $600 new, but under $250 for a warrantied, overhauled instrument.
Buffet's model chart is much more complex than Yamaha's. I'll try to simplify it.
B10: Plastic student model. Don't get this one (someone will ask "why": the keywork's plastic and it's an A=442hz horn).
B12: Plastic student model.
E11: Intermediate wood clarinet.
L-Series "Limite" Advanced intermediate horn made out of blackwood.
C-Series "Conservatoire": Advanced intermediate grenadilla wood clarinet.
R13: Professional wood clarinet.
R13 Prestige: A step higher than the R13 (additional keywork)
RC (Robert Carree): Essentially a custom professional wood clarinet.
RC Prestige: Essentially a custom professional wood clarinet.
Vintage: Essentially a custom professional wood clarinet (for those saxophonists out there, it's essentially a "Reference" version of a 1950's R13, per
http://www.buffet-crampon.com/en/instruments.php?mode=productDetails&pid=95).
Festival: Essentially a custom professional M'pingo wood clarinet.
Tosca: The highest-end Buffet clarinet. Grenadilla wood. Non-R13 bore. Full Boehm keywork.
Greenline: This isn't a selection of models, but how some models are made. It's a resin of grenadilla wood.
Buffet also had a line of clarinets under the Evette (and earlier, Evette-Schaeffer) name. These are fairly old horns.
So, if you step into a dealership and you see a B12 for $244 and a C-Series for a couple dollars more, get the C-Series.
Again, if you're going to buy used, you want to get a recent clarinet that is fully overhauled and preferably with a warranty. If you're getting a wooden clarinet, if the ad says that it has cracks or pins, or has been cracked and repaired, SKIP IT.
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I do not recommend any other make student clarinets than Yamaha or Buffet. Someone else may have a different opinion ....