Welcome to CHR,

'63 Chevy's are some cool rides. They have a big engine bay so almost any motor that you would like could be fit into it. Small block Chevys are a bolt in with minimal modifications needed. I would get rid of the old power glide if you are going to do a motor swap. EIther a trubo 350 as Classic suggested or a newer over drive trans would be great if you plan to travel with it. As for the hydraulics, if you are going to d the lowrider thing I guess that's what you need, but a lot of folks are going to air bags. The are much lighter, are easier to engineer and they can still have a decent ride.

For parts, do a google search on 1963 Chevy parts, you will be amazed. Other choices are Year One, swap meets, and all the auot parts suppliers.

Good luck with your project.

Pat