Well, that card needs a PCI-E 16x slot, which the eMachines T5215 has.
As for the power supply, I would HIGHLY recommend one with more wattage/ amperage. The 8600 GT, though it isn't as much as a power hungry beast like its big brother, the 8800 GT, still requires a lot of power.
Depending on your budget, I would say a 450 watt or higher would be good if you don't plan on upgrading anything else, or a 580 watt or higher if you want to upgrade more things. Better to get it right the first time, and not have to get another PSU later.
I would get this one if you don't plan on upgrading anything else in the near future.