I have some questions about the Marshall TSL 602. Is this a versitile amp? I play a lot of classic rock (Van Halen, Pink Floyd, Jimi Hendrix, Rush, Guns 'N' Roses, Led Zeppelin, Lynyrd Skynyrd, Warrant, etc.) but I also play some shred/hard rock stuff (Motley Crue, Yngwie Malmsteen, Dio, Dragonforce, Judas Priest, etc.). Would I be able to get all those types of sounds from the amp? My guitars are a Gibson Firebird Studio and Epiphone G-400. If you own one yourself tell me how you like it. Thanks in advance.

For the bands you named, I'd go for a JCM800 reissue or a second hand one off eBay. All of those bands use more vintage gear for their tones and the JCM2000 series is a much more modern sounding amp.
The JCM 800s are pretty expensive though and I'm not doing any gigging so 60w should be plenty for me. Besides, I'm looking for an amp that has at least two channels (clean and overdrive) with their own independent equalization. I'm willing to spend about $1,000.
Hmm, I still think the JCM2000 isn't the right choice for you for those types of music. Look for amps with more of a vintage style and feel.
hmmmm, vintage sounds isn't really my forte, I use a JVM410H and though it's definitely a modern amp it's hugely versatile and the poweramp section is based on the JCM800 power amp. Dunno what the cost of the combo models is.

For most of the bands you listed, you'd definitely want to be looking more at british amps. If you're not gigging, the TSL would probably suit you ok, but you might find it to be a little lacking after a while and if you do start gigging, you'll probably start getting much more fussy.

The Vox custom classic series is pretty friendly to your bank account, and can deliver a pretty massive range of classic rock tones.
I'd say JCM 900, or, dare i say a traynor YCV50 and a DOD overdrive?!
That will totally hit the tones you're looking for, and the overdrive would put you over the top for malmsteen stuff, and brighten it up a bit, since the traynor is pretty dark.
But seriously, it can go no farther than hair bands.
So, for the bands you listed, go traynor.
can get one for 600+shipping on ebay.
do it up brother.
Ibanez RG550 20th RFR
Traynor YCV50
Fender FMT HH Tele
Mesa Boogie 2ch Triple Rectifier
2 1x12 custom Theile cabs
ISP Decimator
Krank Kranshaft
Boss BF-2 Flanger
BBE Sonic Maximizer