there seems to be a few for sale that are between 10 and 15k.I think buying one that is done and running is a good start with a few bucks left over to repair/replace/customise to your taste. Building from scratch is way more expensive.
20k from your dad is a huge start.There are way better deals than an old pick up.If you gotta have a 50s Ford then buying an 03 or newer Vette would never make you happy.
Being that you are young,I would think a "ckick magnet" car would be a better buy,,,
Vette,BMW,Mercedes,,,all of these cars can be bought at a screaming deal thanks so much to new north american citizens that buy new prestige cars on a regular basis.