You don't have to wait until they expire! Transferring adds another year to your current registration, and you don't lose anything at all, unless you bought hosting at GoDaddy.

For basic website hosting, I've been very happy with HostGator. For about $7 a month you get unlimited space, bandwidth, and domains. It takes care of DNS for your sites (just point your registrar nameserver information at HostGator's nameservers), has SSH access, provides unlimited MySQL databases, and has a pretty nice interface.