Oil change is a must. Oil breaks down with age. Pull the plugs and pour oil into the cylinders and roll the engine over to lube the cylinder walls.
Priming the oil system is also a very good idea. Pull the distrib and spin the oil pump with a drill. A socket fits onto the shaft. I would spot weld the socket so it has no chance of falling into the engine.
After the cars fires up, and your happy with a running engine, a check and change of all the rubber hoses on the engine/coolant/fuel/brake/vacuum systems will be in order. Remember to clean the oil fill breather cap.
Flush out the brake lines so the master cylinder has new fluid. The master cylinder is likely full of crud, and will tear up the seals if the brake pedal is depressed fully. Pull it and clean it out and reassemble with a kit if you can find one.
Hi Jordan, I am glad to have you with us and have to say it is really cool that you have your grandpa's Caddy. That will make it extra special. I see the guys have already opened the firehose of suggestions and will just say take your time, use the Shop Manual and owners manual, and our website as resources and have fun with it. I mention the owners manual as it has a ton of information, often overlooked, and offers a good overview of the operation of your car. Our Help page has a lot of specific information that has been culled together over the years and can be very useful.
Also be sure to join the Cadillac LaSalle Club (Click Here for more info on joining). Once a member of the CLC you can then join our Free 1963/64 Cadillac Chapter which hosts this site. I would love to share your story of your Grandpa's Cadillac in our Chapter Newsletter!
Again, Welcome to the Site! I look forward to hearing more about your Cadillac. Jason.
As the car has been standing idle for many year, your wheel bearings might be damaged. So be prepared to replace them as well. Don't by the bearings from National buy the SKF bearings. National is cheaper but has been reported as non-reliable.