repeater vs. access point vs. other

depends on the age of the Linksys. If it's what I think it is, it's only a .b/.g router. New routers support .n which has a longer range. As long as your devices has .n then it should be fine.

An alternative to the Powerline is the Ethernet over Coaxial. If you have seen how TiVo/Dish TVs works, it's essentially the same thing. (MoCA network)