Well for a smaller blues jazz type kit there is this from Sawtooth drums on Amazon. I have a great big set by them and I love it. Its easily as good quality wise as other beginner sets like the Pearl Export or the Ludwig Breakbeats. Where it shines is sturdy hardware and a decent set of Zildjian S cymbals.
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If you want different sizes they also have a small bop kit with a 16" bass drum and 2 larger kits one with a 22" bass in a 5 or 7 piece kit or the really big one (that I have) with the 24" bass in a 4 or 6 piece kit. Yeah its cheap poplar drums, yeah stock heads suck but, I was able to easily tune these up and get good sound out of them stock and everything came to me in the mail with no damage or missing pieces. I'm still using the stock heads because they really aren't that bad. I haven't seen drums of this price point anywhere near this quality before.
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Most people will get on here and tell you to look used because you'll get a better value. Mostly I agree. If you can find used drums and cymbals in your area you'll be able to get much better for your money. If, like me, you don't want to deal with other people's smells, pet hair, and spider collections, then this is a solid affordable new option with everything you need to have a complete kit ready to play.
Its the brand Vinnie Appice uses now. He was the drummer for Dio and Black Sabbath. I have one myself and its really nice. I googled around and saw reviews people had made before I bought it. Amazon is about the only place to buy it along with ebay, reverb.com, and godpsmusic.com. If you are in LA than you should have a much shorter shipping time since it ships out of southern CA.
I wouldn't have recommended it if I hadn't had it in my hands for myself.
Also the kits are sold in 3 different "packs" 1)A shell pack which just has the drums and the drum heads, No hardware or cymbals.
2)A shell pack with a hardware pack and a set of starter 2nd line cymbals from Zildjian, the ZBTs.
3)A shell pack, a hardware pack with one extra cymbal stand and a cymbal pack from Zildjian's 3rd line cymbals the S series.
As far as drum sizes standard rock uses a 22" bass drum and either a 12' and 13" rack tom or, a 10" and 12" rack tom. Most kits come with the same size snare and rock styled kits come with a 16" floor tom. If you are more of a jazz blues guy you probably want a smaller kit like this one. If you like really heavy music and want huge drums than they make a larger kit. To start I would split the difference and get the 5 piece I linked before. Its has mid ground sizes between the extreme small and large and can be versatile enough to do both well.
Cymbals has 3 main metal alloys used.
1) Brass
2)b8 bronze
3)b20 bronze
Brass is considered to be the worst and b20 is considered to be the best. Take one major brand like Zildjian. They have lines of cymbals ranging from cheap to Pro.
beginner
1)planet Z - cheap brass sound kinda crappy
2)ZBT (now the i series) b8 bronze better than the brass but still not great.
Intermediate
3) S series this is an odd one with a b12 bronze. Its a pretty good place to start because they sound pretty good for not a lot of money
Pro
4)A series this is what you hear on recordings its a great bright sounding cymbal made of b20 bronze
5)K series this is another great cymbal also made from b20 bronze but it has a darker sound that some say is better for Jazz.
They have many more lines above this but a set of Ks cost about $1k so I stopped there. Cymbal alloys are like this, Brass is Brass that's all. B8 bronze is a mixture of copper and 8%tin with traces of silver. B20 is copper with 20%tin and traces of silver. The higher amounts of tin have a more musical sound and are harder to work with so they cost more.
This is oversimplified because there are other cymbal companies that make high end pro cymbals out of b8 bronze and still others who make crappy cymbals out of b20.