As far as the kind of rope, I was going partly on what I've been told was best and partly on experience.
Polypro fibers don't absorb water (why they used it for underwear) and I reckon you don't want the rope on your oars to stretch when wet, loosen up, and slip around as it works on the oarlock. Unless you park your oars in the sun all season, I wouldn't think UV would be a huge problem. For rope, 303 might be a better UV protectant than spar varnish (which is great for wood oars but isn't really meant for soft flexible things like rope).
Nylon rope might work fine, but it does stretch like hell when wet (noticeable when rappelling on a wet climbing rope). If I tried it, I'd soak the rope before doing the wrap and roll it on wet, then let it dry before doing the final bead of epoxy. It's a lot easier to get and cheaper than the good poly stuff.
About epoxy (also varnish) if you glue the entire wrap to the oar, you'll have a battle getting it off if you need to re-wrap the oar. I put a bead of epoxy (gel quick-set) around the blade end of the wrap, where it gets bonked on the oarlock. The grip end shouldn't need to be glued down if you wrap it tight. And having one end you can take apart might be good if you wrapped it too loose the first try.
Polypro rope comes in different fiber types and braids. Here are two pieces:
The left piece is standard 3/16" all-purpose hollow-braid used for pulling cables through conduits, etc. It's cheap but the fibers are coarse and plasticky, and it's lousy for wrapping oars— might not last a season. (Don't ask how I know.)
The right piece is Sawyer Pro-Line, with finer fibers and strands, and a tighter braid. Although technically a hollow-braid rope, it is softer and gives more cushion to the oars. Costs quite a bit more, but worth it given the labor you put into wrapping oars.
Before machine-braid synthetic fiber rope and rubber stoppers were invented, they wrapped and stopped oars with all sorts of things: laid hemp and manila rope, leather. A couple people posted about wrapping them with webbing.
Rope info is all over the map. I learned a lot when I worked in a climbing & ski shop from the factory reps and sale packets (e.g. the difference between climbing rope and static line for caving). There are quite a few nautical books, like The Arts of The Sailor: Knotting, Splicing, and Ropework by Hervey Garrett Smith, but most seem focused on laid rope and old-timey techniques.
Best approach might be to look at websites for New England Ropes, Blue Water, and other makers, and then pick some terms to use for internet searches. There's probably some grand ropemeister site out there. Let us know when you find it.