Yes, affording it isn't the problem so my top goal is function but less expensive is good as I'd rather spend money elsewhere. Definitely a plus for 3-strand and a minus for braid. I do prefer thinner rope for coiling and takes less space. I'll need to see which thickness works best for the cleats on the bow & stern.
I've been around other people's boats for years and know what I prefer in terms of line arrangements and what I prefer to handle, but I've never had to buy/choose the lines for myself. What you've described was the original plan; Buy 5/8" mooring lines for the club (permanently attached) and 1/2" docking lines to keep onboard. If I don't buy a spool, then I suspect that will continue to be the plan. I definitely prefer handling braided lines but cost and splicing make them less desirable.
Presently the aft locker is jammed with a mash of lines that are too stiff to coil and so shagged I wouldn't use them as a leash for my dog - all of them are bound for a dumpster when I take possession so I'll need lines on day 1.