Welcome to the Forums!
Given the number of years that the coach has been sitting, you will need to consider a thorough inspection and a few maintenance items.
First, an inspection of the "A" frame and hitch components will be necessary to rule out significant rust damage - - surface rust can be expected, but rust though would be dangerous. Also checking visible portions of the frame and axle attachment points for rust through and/or damage would be advisable.
Second, the wheel bearings should definitely be serviced after such a long period of inactivity, and the brakes may need some attention as well - - depending on the amount of attention needed, "fully loaded backing plates" might actually be a cheaper alternative than replacing suspicious parts. Also with the number of years that the coach has remained inactive, the tires should also be replaced - - many Forum members, myself included, have their trailer tires on a five year replacement cycle to avoid tire problems while in-transit - - a blown tire can cause siginficant damage to the side panels as well as bellpan of the coach. You may also find that the trailer has split-rims which will also likely require up-grading to modern single-piece rims before most tire shops will install new tires.
Third, the primary running lights will either need to be made operational or you will need to be prepared with temporary towing lights for the coach. When I picked up my Minuet eighteen months ago, I went prepared with tools and parts to get the trailer's running lights operational as well as magnetic mount temporary towing lights just in case I couldn't get the triler's lights operational. Part of this operation will also likely include rewiring the trailer's connector plug. Airstream's of that period did not use the present industry standard for wiring so you are likely to find that the coach will need a modern Bargman plug to match your tow vehicle's, and you will need to remove the trailer's plug and wire the new trailer end to the current standard. In re-wiring the trailer end of the connector plug, you might find the '64-'65 information very close to what might be found on a '63 if it turns out that the coach is a '63 rather than a '64:
1964-65 Airstream Connector Plug Wiring Color Code
The lack of a "house" battery in the trailer will be of concern in getting the break-away switch operational. A well-charged "house" battery supplies the power to the trailer brakes in the event of a "break-away" situation. Carrying a spare break-away switch might be a good idea as I have had to replace the switches on both of my trailers within a very short time of acquisition.
Fourth, if your tow vehicle doesn't already have a hitch with a ball height of approximately 18" with a 2" (heavy duty) coupler ball, you will need these to be compatible with the early '60s Airstream hitch (assuming that a previous owner hasn't modified the hitch with an aftermarket coupler) - - if the coupler is original, it will likely have embossed on its top surface "Marvel 2"". You will also need a brake controller to operate the electric trailer brakes.
Good luck with your project!