My parents have a G4 tower, it is like 8 years old, and the power supply had died. This is not the first thing that has died on it, just a few months ago the Hard Drive died, but they got a new one. What I want to know is which is the best option?
-Buy a used G4, or other used cheap mac under $600
-Replace the power supply myself, instead of paying $125 for someone to do it. if this option where would I find a power supply for the G4?
-Buy a Mac Mini. (The G4 is only 300MHz, so having only 1.6GHz isn't an issue.

Can someone give me some advice on what they should do?

You can use a standard ATX power supply without too much modification - you just need to swap a couple of wires over on the plug.
http://www.outofspec.com/frankenmac/wire.shtml has the details.
Now, there never was a G4 300, 350 was the lowest speed for the Yikes/Sawtooth models (You sure you are not talking about a Blue&White G3 - they take a standard ATX PSU, afaik), so if it's a Yikes or a Sawtooth all you need to do is connect the grey PG wire (power good, is unnecessary as macs delay start up anyway - on a pc this is the signal which mobo uses to let you know it's powered up after a second or so) to one of the dark yellow 3.3V ones. Then ground the -5V wire - although, nowadays, most high end PSUs do that anyway... not much call for a -5V rail. I've replaced many a G4 psu with an ATX one, it's easy as...
http://www.xlr8yourmac.com/systems/ATX_G4_...TX_case_pg2.htm

the only g4 hard to rewire are the one with a apple display connector on the GPU board (adp).
they even have 24 volt for display wired over the board and the power supply.

Only if you use an ADC card, if you have upgraded to a modern DVI card you can use +5Vsb wire on the 24V power connector pin. You will loose ADC (but if you are still using a G4 with the original video card, than you have my pitty - flash a nice 9800/7800 quick smart), and 9V standby power on Firewire. But, the computer will boot fine and VGA/DVI will work without any problems. If you really, absolutely, have to have ADC; you can use a wallwart (or old ibook/powerbook) power supply to provide 24V to the two pins. It's a minor inconvenience at best.

You can also purchase a PS converter for these "problem" Apple power supplies. $50 and use can use any PC power supply without any modifications.