Your connection will depend on how many people are on the network near where you live and your connection will vary. It is rare for people to get a full consistant 20mb.
Having a wireless router should not make much difference. Any router will slow your connection down slightly, but I doubt most people notice.
Any new cable router that supports 10/100 should be fine for broadband.
Gigabit ethernet will give you 1000 data bit rate whilst fast ethernet is 100.
You should be fine with fast ethenret but if you want to future proof for years to come get the gigabit ethernet.
As for router recommendations, many people here go for Linksys or Netgear routers.
More info on ehternet types here:
http://www.rhyshaden.com/eth_intr.htm