802.11n's finalized now, which means it is the new standard and well worth the investment.
All flavours of residential wifi are backwards compatible, so any new router will work with your ancient Tivo and it's .11b adapter.
If all you want is cheap and effective, the
Asus WL-520GU will do the job, and is very reasonable at $43.
I'd rather spend the $60 on a
Linksys E1000 if it were me, though.
To answer your confusion regarding what the letters mean, 802.11g offers roughly five times the throughput of 802.11b (54 mbps max vs. 11 mbps max). Adding an 802.11g adapter to your Tivo will allow it to transfer data over the network much faster. 802.11n offers theoretically up to 6 times the throughput of 802.11g (~300mbps, depending on how many channels are in use etc) and also offers a nice boost to the range besides, but you'd need an 802.11n adapter at both ends for that as well.