A bigsby is a tremelo system like the ones on strats and the Flody Rose's that you see on the metal/hard rock guitars. It doesn't detune the strings as much as a strat style tremelo or a floyd rose, its more for like an opposite vibrato (as in instead of the pitch raising and lowering with normal vibrato, it lowers then raises.)

As for the difference between hollobody and solid body, its all up to what kind of music you play. If your into blues, jazz, soft rock, or anything around those genres, a hollowbody would be a nice choice for tone as well as looks. If you like to play metal, hard rock classic rock and such, you can't really use a whole lot of distortion with a hollow body as they will feedback like crazy and the tone would be crap since your taking an already great tone and adding gain.