Networking via powerline vs. phone line vs. coax

I'd also say MoCA. It's about the best wired solution you can get without running Ethernet. Not too long ago I used a Netgear MoCA kit to wire up my in-law's guest cottage to their main house since they both share the same cable TV run. It worked perfectly upon being plugged in.

The one downside to MoCA is that it is not nearly as popular as power line networking. Just about every network vendor make HomePlug power line equipment. Only a few vendors offer MoCA compliant devices, and what you can readily find are kits (sets of 2) not just individual bridges, so if you need an odd number you'll have to get one extra. For example Newegg only lists the Netgear kit and it's out of stock. If you live near a Fry's they usually have the Netgear kit in stock, that's were I got mine. Actiontec is the big vendor that makes MoCA devices for Verizon FIOS customers, you can get their equipment new on Amazon and a lot of it used on eBay from Version customers. Missing Remote did a review of the Actiontec stuff last year here.

The last time I tried phone line networking it was a joke (it was also 11 years ago or so), it could barely do an ~10Mbit connection, it usually negotiated a 5 Mbit connection in a newly built home. Which tends to make sense since really you're trying to force wiring that only has 2-pair and was never meant to carry Ethernet data into carrying it. Also you can't really find much HPNA equipment around, it fell very quickly out of popularity. In fact the HPNA group has now moved on to making an Ethernet over Coax specification that competes with MoCA (but isn't compatible with DOCSIS, so you don't want to use it) and is even harder to find equipment for than MoCA.

I have yet to try power line so I can't speak to that personally, but it does seem like the newest generation of HomePlug stuff has some very good signal processing and filtering to help make things work. See the noise testing results in this review from Small Net Builder here.

Also running some Ethernet isn't necessarily as bad as you'd think, it doesn't usually require opening up walls, etc. Slipping the cable under the baseboard molding is pretty painless.