The dryer needs to be more-or-less upright. You can angle it slightly but horizontal placement is not okeh; there have been dryers meant for horizontal mounting, but they are internally different than dryers meant for vertical mounting.
The low side ("suction") service port can go anywhere on the low side of the system and the high side ("discharge") service port can go anywhere on the high side of the system. Place them for convenience, but try and maximise the distance between the low side port and the compressor so you don't have to worry about slugging the compressor with liquid refrigerant by mistake while charging. You needn't make them the highest points in the system, but if you make them the lowest points you'll be creating a nuisance for yourself during system service (oil puddles at the low points).
I am assuming you still have a slant-6 engine in your '63, in which case you should be aware that the commercially-available compressor mount/drive kit is poorly thought out and tends to make problems with underhood interference of the compressor either at the front (too far forward, hits cooling fan) or back (too far rearward, doesn't work with some manifolds and air cleaners). If you don't have factory parts, there is
one (and only one) A/C compressor mount-and-drive setup worth messing with. It's the one designed and produced by Charlie Schmidt; see
here. Check your kit and see if it came with a good parallel-flow condenser rather than a cheap old-type (and no longer adequate with R134a) serpentine variety; see
here and
here. You will need to upgrade the engine cooling system. The stock 4-blade fan will not be adequate, nor will the stock radiator; the engine will overheat and the A/C will perform poorly when the car's standing still or moving slowly. See
here for radiator upgrade info on the pre-'65 cars (w/o radiator support panel cutout for wider radiator core). Shouldn't be hard to get someone to sell you a stock 6- or 7-blade A/C-spec rad fan. Clearance is SUPER tight between the rear of the radiator and the front of the engine; no room for such luxuries as a clutch-type fan.
You will find even a well-engineered and properly-selected and -installed A/C system will have a very difficult time cooling a steel box in the sun unless you give it a fighting chance by keeping some of the heat out. Step number one: thoughtfully pick a good variety of window tint film—not the cheap grey/purple junk; see my comments
here—and have it applied.
