You do not have to limit uploading completely.
Most modern torrenting clients provide a cap for your upload speed. uTorrent is no different. You can click on the "U: current speed" portion of the GUI in the bottom right side of the client with a right click, and then select your desired speed. For example, if your maximum upload speed is 100 kb/s, you could limit it to 50 or 70 kb/s. Experiment, and see what works best for you.
It's enough to cap the upload to 50-70% (this is based on personal experience, you might even set it to 80 or 90%, but I haven't experimented that much) of your total upload speed. That will allow for no distractions while browsing the internet, downloading other things, etc.
Please do not turn off your upload, as you damage the torrent community that way. For example, if you're trying to download a Linux distro (let's say Ubuntu) over a torrent, then you depend on all the people that have already downloaded that file to share it with you. If everyone would just download, and then stop uploading - torrents would die, and no one would be able to download files over torrents anymore.
Bottom line, you can still seed (upload) and browse/download whatever at the same time. Just decrease the maximum speed at which you are uploading to something less than 100% of your upload speed.