Cat5e will serve you fine for 1000Base-T, out to 100m. The standard calls for Cat5 compliance, and all four pairs are used vs. only two pairs for 100Base-TX and 10Base-T. Anything better than Cat5 is just future-proofing...
The networking gods worked it out that 1000Base-T had to run over Cat5 as a minimum because there's an awful lot of Cat5 cable out there in the walls right now. They decided that they didn't want to make everyone re-pull cable yet again (as happened when Fast Ethernet was introduced, and everyone had to junk their old Cat3 10-meg Ethernet or Cat4 16-meg Token Ring cable plants and move to Cat5).