I think Cat 5e is sufficient for most people, at least for the next several years, by the time faster home networking is practical you'd probably want something that is better than cat 6 anyway.
Figure out where you want your server to be and run all the wires to that location and terminate at a patch panel, it's generally not recommended to try and crimp an RJ45 plug to terminate in wall wiring because a bad crimp is more likely than a bad punch down. I just wired my home for cat 5e and used keystone jacks, wall plates and a patch panel from Monoprice.com, they've got the best prices you'll find. If you don't already have a long, flexible shank drill bit I'd suggest buying one before starting the job, I didn't and looking back I could have saved myself several trips through the crawl space if I had. I used the blue plastic "old work" electrical boxes, but there are more expensive orange boxes that are made specifically for low voltage applications such as Ethernet, either will work, and are pretty simple to install. The blue boxes have a tab that holds the wire from pulling out of the box, for regular high voltage wiring the code says that the wire needs to be secured within so many inches of the electrical box, the tab satisfies the code, but for low voltage the code doesn't specify so I bent the tab back and out of the way, it made pulling the cable a lot easier. If you've got money to spend invest in a good punch down tool that trims the excess wire as well as doing the punch down, it'll save you some time. If you are on a budget, you'll probably find a cheap plastic punch down tool that is included with the keystone jacks and/or your patch panel. Use that cheap tool and a utility knife to trim off the excess wire, I don't anticipate using a punch down tool enough to justify the $50+ cost, after installing the last jack I started thinking how nice it would have been to have the right tool though. I used a sharp knife to strip the cable jacket and probably wouldn't spend money on a stripper designed specifically for Ethernet cable.
As far as I know there are no fire/safety concerns with Ethernet wiring, it's low voltage and considered pretty harmless if it fails or is improperly installed. If you plan on running the wiring through heating ducts for some reason you do need to use plenum rated cable. Standard cable has a PVC jacket that releases toxic fumes when burned, the plenum rated cable is supposed to be less dangerous when it burns. I can't think of any reason to run cables through heating ducts in a residential installation.
While I was at work running Ethernet I went ahead and pulled an extra cable and installed an RJ11 style keystone jack for telephone, I figured for now it's nice to replace all the surface mount boxes in the house with nice flush mount jacks, I've only used 1 of the newly installed phone jacks, but if I find a need for additional Ethernet jacks in a particular room I already have wiring I can use, I'll just have to change the keystone jack to an RJ 45 and move the termination to the patch panel.
