BitComet is banned from many private trackers for a good reason. It has a way of damaging the swarm to your benefit, hardly the right way to encourage the sharing spirit of BT.
Use uTorrent (small and easy on resources, great first client) or Azureus (does everything and anything, but until you're experienced this is irrelevant) and make sure you forward the ports. Also, you might want to try PeerGuardian to help make sure that nobody montiors what you're up to.
The difference you will find strange is the way torrent sites work as opposed to LimeWire etc., you have to download a small file to start the download, but it all works P2P after that. Oh, and get an adblocker if you're heading over to mininova.
UPnP is the ghetto fix for when you can't get port forwarding to work, but it works none the less.
The reason it slows down your internet is because you ONLY HAVE SO MUCH PIPE. Think of it like this...say you have a 3 inch water supply line. Normally, there's maybe a quarter of an inch coming through, so every little bit has room. Now you latch onto a fast moving torrent, and there's 2 and 7/8ths inches of water coming through....doesn't leave much space for other traffic.
Random port on uTorrent only works because you're using UPnP, if you were forwarded, it wouldn't work. And randomizing the port doesn't work because you're forcing it to switch to a NONMAPPED port. :)