I think that
1, try connect to isp broadband using router that incorporates broadband modem, not a wireless one to avoid clashing wireless signals, simple 4 port router/modem
2, run cat 5 cable from router/modem upstairs to wireless AP.
I've set it up that way before, so it ought to work, but,,,
make sure that the router/moden you use in basement does not have wireless function, or else you might get clashing signals