First, anything is possible with enough money behind it.
Having restored a few cars in my time, it's not something you want to pay someone else to do unless you're obscenely wealthy. It can be hundreds of hours of labor, thousands and thousands of dollars in parts, NOS and reproduction, and depending on the car, hours of detective work to find parts, long car trips to weird backyards of weird people in weird parts of the state with a sawzall to cut the roof off another vehicle (yes seriously) and then the teething stuff that happens as you just try and drive the goddamned thing and find all the stuff that didn't quite go right. Let's not even discuss what happens when someone hits your '73 Opel Kadett Rallye. It's not like you can pop on to the internets and order up some new panels like you could for a '08 Camry (or hell, even a more common classic like an F-body.) And this is all if you're mechanically inclined, and have a best friend with a full shop as well as a body and paint guy to consult.
If you want an older car, your best bet is to find a nicely kept one. It's not impossible - I bought a 16 year old Jeep Cherokee last year from an owner that bought it new, parked it in the garage, and took it back and forth to church on Sundays. 32,294 miles over 16 years with oil changes every 3 months and regular servicing all written down in a little book. That is absolutely as good as it gets and is a one-in-a-million find. I would add that this took two years for me to find, checking CL in a 3-state area twice a day, and I paid out the nose for it because I was the 30th phone call they had received in an hour from posting it, and drove 3 hours each way to get it. (This is because Cherokees are awesome, coveted, and last. Other vehicles probably won't be as crazy.) But in the end, you'll pay more than the vehicle books out for, and in the end you own a ~20 year old vehicle that's maintenance heavy compared to a newer one.
TL;DR: If you don't turn your own wrenches, old cars aren't for you.