I'm a brand new player too (hi all), and am playing on a system that is nearly 10 years old (except for the graphics card).
Core 2 Duo E6850
Nvidia 650i motherboard
GTX 470 graphics card (bought off ebay second hand for £27 after my GTX460 (which was a replacement for a 8800GT) died)
8gb standard RAM (I used to have 4gb quicker RAM, but switched it out for more)
Vista 64
As you can see, I'm well below minimum requirements in some areas, but it runs absolutely fine. The game's recommended settings were for 1600*900 at high quality... I changed that immediately to 1900*1200 (my monitor's native) and medium settings.
Graphics cards make a huge difference, in all games that need them. Don't skimp. If you're money constrained, doing what I did and buying an older card second hand is always a good option. Do do research on benchmarks though.
I'm 37, and probably was a little young (7 or 8) when I first played the original Elite on both my friend's BBC and my C64. Never really got the hang of it, but I do remember docking a few times successfully.