CAT5e is all you need if you only have a gigabit switch and gigabit NIC's. Gigabit is roughly 120 Mega Bytes per second and CAT5e can do this easily.
CAT6 can do everything up to 10Gb/s or 1,200 Mega Bytes per sec but you'll need 10Gb switch and NIC's to be able to transfer at that speed and then you'd also need the drive in a RAID0 or RAID5 setup to get up to those speeds. A normal HDD is around 120MB/s read/write.
Now all that being said I wired my home and office with CAT6 just because the price difference between the 2 on a 1000' bulk isn't much at all.
Also remember your fastest speed will equal the slowest piece in the network.
If the network is going to be in one room this should be a fairly simple setup.
Just to keep the price down I'd suggest going with mostly Monoprice equipment. It is good stuff especially for the cost.
A small 8 port Gigabit switch
http://www.monoprice.com/product?p_id=10927
If you don't want to run cables inside your walls, another suggestion would be using a cable raceway. You can run these around the walls just above baseboard if you have that, run the cable inside and even paint match to your wall color so it blends in better.
Similar to this. Cable Raceway can be picked up at either big box home improvement stores with 90 degree bends, T's and pieces to join them together. Most of them just use double sided tape already installed to stick to the wall.
View attachment 590961
Measure from the place you would put the switch, down the wall, then follow around the wall to the first computer and on to the second and third. Add a few extra feet to the measurement to be safe.
You can get a 50ft CAT6 cable from Monoprice for less than $10.
http://www.monoprice.com/search/index?keyword=cat+6
Run 1 cable from your internet router out to the gigabit switch. Then 3 cables out of the switch to the two workstations and the server.