I use .010 - .046 GHS Boomers (might upgrade to 11s and see how they sound/feel) and DunlopNylon .73mm picks. Those picks don't dissolve in your hand like the colored Dunlops. I got a set of 12 a couple years ago and i still use them, with very little wear.
I like the medium gauge picks because they don't flop around, but they'll bend if I accidentally hit a string too hard. Haven't broken a string that way in over a year (knock on wood). As for strings, it's the same thing everyone else has said. I like to be able to really dig into my strings, for that extra bite. I don't play live much, but I keep my gauge the same as for recording. The thicker strings don't break as easy, plus they sound good. It's just a matter of getting used to them being thicker. That said, I wouldn't play on 13s or 14s like my uncle, but then again, he's a blues guitarist and I'm a rock guitarist. It depends on the sound you want. The thicker you go, the less the pitch fluctuates when you strike the string. You need that little bit of waiver on string contact in rock in order to get that aggressive sound.
I've found that lighter picks mixed with heavy strings sound very dull, and then heavy picks with light strings break way too easily. So I found a middle ground between the two that I like.