Welcome, Doug.
Sounds like a neat truck you got there. You have a few options on the wheels/tires. Stay with the 17's which should do you fine, replace the wheels with later 1 piece 16", though you may have to hunt for a set with the right back spacing for tie rod end clearance in the front...might not be an issue on a '60 but I'm not sure, or find a set of 19.5 wheels and run tubeless radials. If you go with an 8r-19.5 tire they will be about the same height as your 17's.
Post pictures!
