10's+ get you a heavier sound but are harder to play lead with when it comes to bending and sliding. The thicker the string the better the core tone but that's something you will only really notice after years and years of playing - and you only really notice it when playing through a serious pro rig. Lighter guage suit lead guitarists and are the most popular for speed playing. They are easier to slide over and easier to bend plus they don't punish the fingers as badly as heavy strings. Jason Becker used to only use 10's and I know Vai usually ends his tours on 10's too but a lot of other great guitarists go lower eg Malmsteen as mentioned above.
I use 10's on my 7 string for rhythm and 9's on my Jem for lead. Untill recently I only ever went with Ernie Ball SUper Slinky's but recently I switched over to Elixer sets. They last a hell of a lot longer and always feel smooth even if you've been sweating all over the fretboard. I notice greater sustain with them too but that could just be the power of suggestive marketing;-)
As far as picks go I only ever use 0.8mm hard picks, for me they create a clearer pick attack and that helps for fast playing. When it comes to picks there is no magic formula, just whatever works best for you.