I would say go with choice number one out of what you provided. Wireless repeaters cause a lot of issues if you are just repeating crappy signal. If you can put a wireless AP in your basement, then you might as well run some cable, buy some crimpers and RJ-45s, and just hard wire your PC. Especially if you do a lot of stuff that is sensitive to latency like voice or video, I can't stress enough how much better a wired connection is. Wireless really sucks, especially if you have tons of neighbors who also use wifi, because there are only really 3 usable ranges out of the 12 channels you can choose, and it is really easy to get interference. Microwave ovens, baby monitors, bluetooth devices, neighbors with strong signals, etc., all can cause you headaches. Back in the day everybody kept their stuff at the default of channel 6, but nowadays most people know to change it to a less utilized end of the spectrum like channel 1 or 12. Another free option would be to move your wireless router to a better location somewhere in the center of your building, especially if you can put it in a hallway or somewhere similar that minimizes the number of walls the signal needs to pass through.
