The big Gibson hollowbodies always come to mind when i think of solo work. Joe Pass with his ES-175 and Tuck Andress and with his L5 are two of my favs. Although you usually see hollowbodies, don't limit the selection to them. It's all about the sound you're after (as mentioned above).
I do a lot of solo shows and have been looking at the Del Ray guitars...pretty cool and somewhat unique. I'm trying a few out locally today so I'll get back to you on that one.
As others have mentioned, the Gibby style hollow/semi-hollows are great for this type setting. I've also used Teles and Les Pauls in the past. I'm putting together a strat project right now so we'll see how that that works out but I've always thought it just didn't look right to be standing up there with nothing but a strat.
As for amps, all of the ones mentioned above are fantastic. I recently had (and sold) a Blues Jr. tweed model that would be cool for those type of settings. The Peavey CL30s and 50s are nice too but a little heavy. I play through the BOSE L1 system and can get some great cleans out of it in the right room. Most of the time I mic up a small tube amp and turn it to the wall though.