If I use the Cat6, it's cuz I got 1000ft for free.
5e is fine, it won't matter either way. Both samples I have are the same as far as flexibility goes. Cat6 doesn't need to be overengineered, it just tends to be. Mil-std is overbuild no matter which type I get.
The best powerline isn't going to approach Gb speeds for LAN transfers. That plus the pricetag steers me away unless absolutely necessary. I've tested what is supposedly the best system, and it's fine for 100Mb networks, but it doesn't approach Gb capabilities.
The basement is ground floor and it's an apartment. The house is 3 stories. Unfortunately the cable feed is in that closet, so it all originates from there. The only other idea I can come up with is putting the cable modem and router in a room on the 2nd floor and drilling up to the 3rd floor and down into the 1st floor. I guess that's doable. Less holes and cutting.