1. According to Tom Hardware's May 2008 videocard hierarchy, your 8600M GT is slightly more powerful than my plain vanilla 6800, which allows me to run the game fine, at the highest visual quality (but with no AA & no bloom effects).

May 2008 Videocard Hierarchy

2. 3GB of RAM is more than enough.

3. What GHz power is yout Intel processor ? (But it should be OK.)

4. I suppose than your OS is Windows Vista. If you had any problem, I would point towards Vista. Update Vista + update your nVidia videocard drivers (at least to the December 2007 drivers).

Go ahead, buy the game, but do update Vista and your drivers.

And before launching the game ... close most user-defined background programs (except, of course, explorer.exe).

Sins of Solar Empire is the game which can be played on much low-end machine.

You will have no problem with the highest setting.

Man, I miss the days when it was GeForce 2, GeForce 3...

My computer has a GeForce FX5700, which is several generations older than yours, and I can play Sins. I think mine is technically lower than the minimum requirements. The only time I have any problems is when I try to zoom in on massive battles.

I suggest downloading the demo first. If it runs the demo it will run the full game just fine.