It would help to tell us what your computer is when asking for help. Is it the Envy 800-060?
If so, your 600W power supply should be fine as long as it has an 8 pin power connector for the card.
As far as available space to fit, you will have to measure the length of space inside the case and compare it to what ever cards specs you want to buy. If there is enough space, you should be good to go.