How spendy do you want to get? You could go full custom and get a made to measure steel frame and build it up with with modern parts that is still classic/retro looking.
Or, and I'm a fan of old steel frames with modern bits that look classic, but have modern brakes and 20 speed drivetrains, so I'd prefer ths option, is getting a nice Italian or British steel frame from
Ebay with 130mm rear spacing so you can whack in a pair of modern wheels (or retro looking silver ones if you prefer) and something like a Shimano 105 double 22 speed groupset , so you've got a fairly classic looking bike that rides like a modern bike (compared to your 60's racers) that has spare parts available from any local bike shop/online that you can easily replace as rack up the miles and wear stuff out. Find a nice frame and you've still got a pretty unique looking and lovely riding bike for cheaper than the cost of a boring off the shelf, made in their millions Specialized.