A 396 should bolt up fine, but you may want to consider a trans with a bit more guts if you're going to run a big block. Not 100% sure if those mounts will work, but the chassis is similar to the '67-'72 which did have a bog block option, so setup should be the same.
For the diff, look for a tag the says "Limited Slip Fluid Only". Or, if no tag, jack the truck up and set the axle on the stands with the trasn in neutral. Try spining a tire by hand. If the turn in opposite directions, it's not a posi. A note if it is a Posi, parts might be hard to get, as the '63 is the early version of the 12 bolt with the 17 spline axle. From what I understand, the clutch packs are not being produced for that alxe, 30 spline (mid-'65-'76) only.