I usually go with whatever's on sale (typically Ernies), but if I feel the need to splurge a little, I'll go with Elixirs.
Thickness, I go with
Skinny Top/Heavy Bottoms for those chunky 5th chords and extra djent-y palm mutes in C or B. So... 56s/52s for my heaviest and usually 10s/9s for my high Es. The ones I have on my Jackson currently are 52s-10s, the Skinny/Top Heavy Bottom Ernie Balls. On my ESP, I have 42s-9s, if I recall. May be 46 for the low E.
Always, always personal preference, but thicker strings come with the bonus of helping you build finger strength, so if you ever go to a smaller gauge, you'll be able to get some ridiculous bends.
Also, if you're serious about playing, I recommend investing a few dollars in
a hand grip. You can either grab one on Amazon or at your local sporting goods store. I'm sure Walmart and Target will carry them, too.