Cat 5e is cat 5 with a slightly improved design that should result in less crosstalk (electromagnetic interference). If you just have a 10Mbps network (unlikely, unless you have an old router/switch/hub), it won't make a difference, but Cat 5e might perform better if you have a 100 Mbps network. Additionally, if you have gig (1000 Mbps), I don't even think the original Cat 5 can handle it, but Cat 5e can. Basically, between the two, Cat 5e is your better bet. (I think it's actually difficult to find original Cat 5 cable these days, but I could be wrong.)
Cat 6 is going to be more expensive and probably not worth it unless you are laying non-easily-replaceable wire, say, through your house (or unless you don't find the cost difference that significant). It might handle gig a bit better than 5e, but both are perfectly acceptable; cat 6 (unlike 5e) is expected to work with future 10 Gbps networks, but I assure you that will not matter, especially at your house, for some time to come. 😀 As for the differences, it's basically the same cable, but it improves the speficiation to further reduce crosstalk and noise--but all three of these cables are made with the same number of wires, same materials, and are backwards compatible.
Basically, your best bet is probably 5e.
