That wire is a 14 gauge wire and should be fine to drive those speakers without any issues at all at typical distances for left/right speakers.
No amp recommendations from me. I do find the used amplifier market to typically be of much better value overall, but I'm not sure what you have available to you or what you intend to use as a source or if you want to connect things to a television as well. Some details of your intended use case would be helpful. I always have my speakers connected with a television as well, or they are part of my distributed audio, so I have surround receivers (Yamaha) and Rotel amps that I picked up used that sound great. Rotel stuff, even used, may be a bit over your budget.