I have a 1968 Peugeot PX10 and there is lots of information about these bikes as they are collectable but they are French so many of the parts and advice are specific to this bicycle. Here are my suggestions:
1. Find out why you are getting punctures - bad tires? nicked or dented rim? old rim tape? etc.
2. If you really want to get new rims, find out what year your PX10 is and then what rims, hubs, derailleurs, cassette/freewheel, tires it currently has (or just post photos).
3. Familiarize yourself with terms like tubular vs clincher rims, cassettes vs freewheels, french thread freewheels, Simplex gearing.
4. Decide how committed you are to keeping the original classic look and feel of the bike or if you value more modern practicality.
The best place to then ask the question is in the "classics and vintage" section of this forum:
https://www.bikeforums.net/classic-vintage/
PS- my PX10 has new 700c Sun M13 rims (in silver) which look very similar to the original rims and are cheap and easily available. The hubs are used 36 hole Normandy high flange hubs which are common as they were used on many bikes of the 70's like Raleighs & Schwinns but look almost identical to the PX10's Normandy Competition hubs.
