I run my CB from a fuse tap on the fuse box. I had it wired through the stereo but I cleaned that up when I replaced it. Optimally, you'll want to run it straight to the battery for the cleanest signal. Sometimes you'll pick up engine noise in the CB.
For the antenna, you have a few choices. I'd probably route the cable like teh 3rd brakelight so it neat. Otherwise, you'll be pinching the cable in the tailgate if it's just hanging. I don't like mounting the antenna on the tailgate since it's a bit more difficult. The cable will need to come up from the passenger side.
For the fuse, it would depend on the CB. If it's an old one as big as a fridge, it might. I'd guess a 10-20a though. You'll want to track down the mfg. to see what it uses.