Cable's not fast. Sorta just lies there actually. 🙂
You can use any type of cable you want. There's no such thing as "too fast" a cable type, except insofar as coax networking is slower than UTP, and you can't use UTP on a coax connection.
Cat5 is the minimum for 100Mbps FastEthernet. Cat5e is slightly better signal quality and technically supports gigabit over copper, but Cat6 would be better for that. Cat3 is only 10Mbps Ethernet.