Just about every computer these days uses a standard ATX power supply you should not need ant adapters at all to use it in a different machine. If its an older motherboard that uses 20 pin motherboard power connection most power supplies have a detachable connector for that reason.
If you do buy a better PSU keep in mind if you will be using a better GPU in the future for higher end GPU's you will need more powerful PSU's.
Keep these brands in mind.
Corsair, Antec, SeaSonic, Enermax