[Butcher]

Well using dT = (1 - Q/Qmax)*dTmax (which is a rough measure of dT for TECs) and assuming a 100W heat load gives:
dT = (1 - 100/156)*67 = 24.05C for the 156W
dT = (1 - 100/226)*67 = 37.35C for the 226W
So on the face of it the 226 looks much better. However you have to sink more power. Assuming 75% efficiency the load is:
Qtot = 100 + 156/0.75 = 308W for the 156W
Qtot = 100 + 226/0.75 = 401W for the 226W
If we then assume a 0.08C/W system and 25C ambient the hot side temps are:
Thot = 25 + 308*0.08 = 49.64C for the 156W
Thot = 25 + 401*0.08 = 57.08C for the 226W
This gives a cold side temp of:
Tcold = 49.64 - 24.05 = 25.59C
Tcold = 57.08 - 37.35 = 19.73C

Now, unfortunately I have no idea what the actual C/W rating for your system is so that is fairly rough - if you cooling system is worse then the 156W is going to be better, if the cooling system is better than the 226W is better. also if the heat load is much greater than 100W then the 156W will be inadequate. For reference a P4 2.8 puts out 75W stock, overclocked to 3.5G without adjusting the voltage means approximately 94W of heat load.

To get to 0C on your P4 with a 156W would require a perfect cooler (or very low ambient), so I don't think it's going to be adequate for your needs. With the 226W you'll need to keep the hot side at 37C or less, which will require a cooling system capable of 0.03C/W, which is no easy feat!

ATX supplies can work - you'll be hard put to find one with enough 12V I suspect. To get one to run you can connect the grey and green wires (I think) and it'll power on. You'll probably need at least 1A of 5V load to get proper operation out of it.