I've just bought a new guitar and amp (LTD EC-1000VB and Tiny Terror Combo 12), both second hand.

I'm gonna have the guitar set up by a guitar shop to make sure it's as good as it can be before I play it, which will involve new strings, but I don't know much about the difference between string types.
So what's the difference between string brands and gauges etc?

Also, with the TT, is there anything I should be checking when I get the amp? Tubes seem to need a lot more care than SS so I figure theres probably something I don't know.

Also, in terms of care, apart from the obvious stuff (dont get it wet, hit etc) and the standby mode issue, is there anything else I should be doing?

Regarding the tubs: Just don't knock your amp around incredibly harshly, because I believe the tubes will be the first to break.
When turning the amp on, turn it on, give it 20-30 seconds, then turn the the standby switch on and start playing. When turning it off, do the opposite, turn the standby switch off, leave it for 20-30 seconds, then turn the amp. This allows for cooldown and warm up.

Strings: String gauge is the thickness of strings. If you have thicker strings, they will be tighter on your guitar. For lower tunings you have thicker gauges. For an E standard I go with 0.10's (The E string is 0.10cm thick, then the rest of the strings thicken in somewhat of an order). They can handle d standard/ drop c kind of. For drop c, probably .11's or 12's would be fitting. B standard and stuff would be 13's or maybe heavier, im not sure.

Brands, Im not really sure, just quality I guess. Go with Ernie Balls though, they are pretty standard, and cant go wrong.
Sounds good. I mainly play stuff between E drop C area, very occasionally going down into B, so would .11s be a decent way to go?
11s should be fine, larger strings might require some nut adjustment to allow for the thicker gauge, congrats on the esp, i absolutely love mine. haven't played a tiny terror but everyone I have talked to tells me they are amazing. Congrats!
Gibson LP traditional and DC standard, SG standard, MIA Standard Strat, Schecter Banshee 7(*for sale*)
EVH 5153, Orange TV50H 2-2x12's
Line 6 M13
Thanks, I was quite lucky and found two very good deals on ebay at the same time, and on the eve of my birthday :P So I just went for it. Parents were kind enough to buy me the guitar and I gifted myself the amp

Everyone seems to love the EC-1000. The guy at the guitar shop where I tried it out loved his so much he had a tattoo of it on his arm :P