I tried a couple different torrent clients, ended up switching back to Azureus because while it tends to slow down my browsing it also gets about 10X+ the download speeds, even for 'overnight' tests. It would even get connections and download where other clients wouldn't.
And yes, I made sure first that I had the other clients set up with my NAT firewall.
When I want to browse/play online games I simply shut it down.