If it's a managed switch, you can shape the bandwidth per port (egress/ingress). Depending on the switch, you might have to enable port based VLAN. You can also configure QoS on the router as mentioned by others too but that might too much of a load for the router if it's a cheapy one.
BTW, which switch did you end up getting? I might be able to help you out with the config.
Netgear GS108T is what i ended up with.
The two options I saw were to set port speed (i.e. 10/100/1000) and then to set a kind of priority scale - 1 to 7. I ended up putting the xbox with top priority, the others computers in the middle, and mine at the lowest.
We have about 16 active internet ports in our house, but most of them are printers, NAS for backup, stuff that gets intermittant use. I hung all of those off a single port to another switch.
I don't think I need to configure VLAN as my traffic issue was really about prioritizing internet traffic (specifically latency) rather than overall exceeding the bandwidth of my network. Almost all my traffic is to the net, very little is between individual computers on our network.
By hooking this switch to my Apple Airport Extreme, and then running everything from it, I seem to have solved the problem, at least so far.
If there are things I can do further, I'd love to hear suggestions, as I said I'm sure I've just touched on what this thing can do - a lot of the terms in the setup process I had never even heard of