Flat pick most everything; do some fingerpicking sans pics.
While I mostly play classical-style, on electric guitar for jazz and rock I like the flat pick. I use different gauges for different purposes: heavier for a fat tone for playing single-note lines, lighter for strumming passages. Jim Hall does a similar thing. Try all three gauges and decide which ones sound best in which situations.
I use a flat pick about 50% of the time. Some songs are better with finger style while some just work with a pick or a hybrid style of pick and fingers.
flatpick here, 9 years in and never could seem to get finger style. I love the sound though so hopefully one day :P
I finger pick a few songs but some sound better with a flat pick, so for me it depends on the song mostly, I tried a thumb pick but was sort of awkward, I normally use a softer pick (under 1mm) so the the thumb pick was a bit too hard, so I really didn't give it a chance. Also I find if I'm playing wirth a few folks, sort of jammin, a pick is easier to keep up with the song.
I always use a Doyle Dykes thumbpick or just my fingers if I am
Hybrid picking for me, just can't get used to a thumbpick. But I like to be able to go from Travis picking style to lead style and having a flat pick really helps for that and just works better for me personally.