The car in the pictures is going to be a big project requiring a lot of cutting, welding, straightening, fabricating and other work you may or may not be able to perform yourself at home. If you just want to put on parts, keep in mind that new old stock for these cars keeps getting harder to find every day and therefore a lot more expensive when you do find it. You can put on parts that are after market, but that will bring it's value down even more.
I think you should consider just keeping it as is for sentimental reasons and getting a different one if you want a driver. Once you do all the work, is it the same car Grandpa and Dad bought?
It's like your Grandfather's axe story. Granddad gives you an axe and one day while using it the handle breaks, so you put on a new handle. Then years later, the head cracks, so you put on a new head. Is it still Grandpa's axe?
I suppose it is answered as much by the heart as by the head.
You can get a car in that condition for around $300.00- $900.00 though, so there's that to consider.