The only things that might be effected by using wireless are
Amazon: download speed (quality unaffected)
Tivo-MVR transfers: transfer speed (quality unaffected)
BUT, as BruceShultes pointed out, these also depend on a) the speed of your wireless network and b) the speed of your internet service (except that Tivo-to-Tivo MRV and TivoToGo transfers only care about your wireless speed, not your ISP).
If you have the Tivo Wireless G adapter and an 802.11g or 802.11n router ("wireless G" or "wireless N"), you should have plenty of network speed for all of the above. And if you have 5mbps or better internet service, you should get decent (if not always best) Netflix quality.
If you have DSL and 802.11b (basic wifi), then you may experience some quality issues with Netflix, and your Amazon downloads will be pretty slow.
As for whether you should use a wireless bridge -- I tend to think you should try the easiest solution first and see if it works for you. Just get the Premier working with wifi, and if you notice that transfers are too slow and your Netflix shows just aren't the quality you are expecting, then try the bridge. A lot of people use the S3 on wifi-only and their results are just fine.
"Mmm... forbidden donut."