My preference would be Cat 5e for general cable runs and Cat 6a for long cable runs where PoE or 10Gbps is required. Both officially handle 1Gbps over a 100m run (328ft), but can usually handle up to 10Gbps over shorter runs. Cat 6a cable has thicker conductors than Cat 6 (without the 'a') and is rated to handle 10Gbps over a 100m run.
I did the mistake of buying Cat 6a cable for our home wiring, only to spend a few hours troubleshooting and recrimping RJ45 plugs wondering why I could not get all 8 conductors to link. It turned out that the pack of "Cat 6 plugs" I bought where actually Cat 5 plugs falsely described as Cat 6 in the Amazon listing. This turned out to be the case with many listings I looked at based on the user reviews (sort by Newest first). Even when I got hold of proper Cat 6 plugs from a local trade supplier, getting the 8 colour coded wires aligned up is a lot more awkward than with Cat 5e as the thicker conductors are stiff.
Basically, unless you need 2.5Gbps or faster over very long cable runs, I would choose Cat 5e for the ease of installation and termination and the high risk of buying Cat 5 plugs / wall plates falsely described as Cat 6 capable. In any case, Cat 5e will provide vastly improved throughput, latency and stability over any Wi-Fi or Homeplug based connection, particularly over longer indoor ranges.