does the number of things running on the router make it any slower
Unless you're planning on using every single port on the device, with each computer being used by different people at the same time.. no.
A router simply routes. It's not like a VCR where the pass-thru picture is degraded from each device added to the chain. If you have a super-fast connection and all the computers are using bandwidth intensive stuff.. like.. oh I dunno, serving files or streaming high-def movies from reel.com or something.. nothing is going to happen.
Now if you actually DO have heavy usage then network collisions and router memory are a concern: Then simply buy a more expensive/better router. Oh, and have fun setting up wireless security if you're going down that route. Ugh I hate wireless. Always a pain copy/pasting WEP keys and neighbor-proofing the setup.