I think a few years ago I've dealt with replacing a power supply in a gateway like this. The plastic outline of the power cord jack on the power supply may be partially covered by the back of the case, so it won't sit flush, but you can still jam the screws in there to secure it well enough.
Most power supplies out these days are 300+ watts, which should easily be enough to cover even the most loaded down P3-based system. Too much wattage will not cause any side effects.
I agree with the above, don't get the cheapest one you can find because in the end, you get what you pay for. Spend a few extra bucks and get an Antec. If you really want to wow anyone, I know Antec has one with a few LEDs in it to cast a nice blue light behind the PC. Because when it all comes down to it, anything with a blue LED is faster, cooler, and way better than anything else
Also putting the PC on a UPS might not be a bad idea. I've seen brownouts cause power supplies to croak.