Ordinarily I'm all for doing your own work on your own guitar, but unless you've done major work to a guitar before, I'd take it to a good luthier. Even a minor alignment error and you've got holes in your guitar that will ruin any resale value it has. That being said, if you're willing to take the risk, a bigsby shouldn't be too hard to install if you've replaced a bridge, shimmed a neck or slotted your own nut before. It's all about getting it located and mounted correctly the first time.

Floyd Rose also does the FRX, which can directly replace a Les Paul style bridge.

I've replaced tremolos with aftermarket models before, but it was always a drop-in replacement because I'm not comfortable doing anything crazier than drilling bigger holes for tuning machines on my guitars. One botched measurement or slip of the hand and you've got a permanently ugly guitar.

There's also this trem for the Tele which requires no new holes