if it's a new computer with decent hardware, it should run the current flightsimulators.
The main civillian flightsim out there at the moment is Microsoft Flightsim 2002 (its replacement has been announced and will be released sometime next summer).
Flightsim 2002 should be going on discount soon if it isn't already to keep sales up while people wait for the next version. It's pretty good already so you might as well go for it if you can get it cheap (or if you don't want to wait half a year before getting started).
- Most good computer stores will have joysticks, but for the better ones (and yokes, rudder pedals, etc.) you're likely limited to either mailorder or specialty stores. http://www.avsim.com
is a great site with their own online flightsim store (all proceeds go towards running the site) which is an option if you're in the US (import duties make it less nice in the EU).
Basic operation isn't hard to learn, but does take practice.
As in real flight training, start out in a small aircraft flying circuits and build up from there. Most people who give up take huge steps and fail and get frustrated.
Start with the basic FS
and maybe some downloaded scenery. After you can fly the default Cessna and Baron, start looking for some quality addon aircraft like the Archer and Cardinal from http://www.flight1.com
Only when you can fly light aircraft well is it really time to move on to airliners.
The best there are provided by http://www.phoenix-simulation.co.uk
In my experience most of the best aircraft addons are payware. While there is good freeware out there, most is not as good by far as the commercial offerings (especially the panels and flight dynamics are usually lacking).