Hey! I had a '63 Spyder back in 1975, sorry I sold it. I can't add much to the list, but I'd check the generator, blower (on top of the engine) and idler pulley to make sure they spin freely. You wouldn't want the belt to be dragging on any of them.
If you get it running, be sure to check all brake components. That puppy is before they had the split diagonal hydraulics. The brake hydraulics are a single system, a blow-out anywhere, and NO brakes. To that end, I'd also make sure the parking brake is fully functional before you take it out.
Also, a word on tire pressure. The fronts take a lot less pressure than the rear, there's almost no weight on the front. One of my old Corvair books shows 15 PSI front, 26 PSI rear. It's important for the handling. Also about handling, DON'T drive with too much "spirit". The Corvair will lull you into "I can take that curve at any speed", you can't. When the rear end on a Corvair breaks free, it comes around with a vengence (voice of experience). It's a rear-engine thing.
Maybe I got a bit ahead of things. Wishing you good luck on your project, keep us posted.