That will be fine. Unless you've installed a PCI-e card since getting the computer, or special ordered one when you bought it, there will be a free PCI-e x 16 slot. You can insert the card.
As far as power, 600 watts will be enough. You just need to make sure there are two 6-pin power plugs coming from the power supply. That's what the card requires in order to be plugged in. You might also have 8-pin connectors in the form of 6+2 pin connectors. Those look like a normal 6-pin with a small two-pin connector that you can either leave unused or use for an 8-pin connection. Either way, you'll need two of either.
If you have those things, you'll be able to run the card.
Enjoy!