Yes, it's awesome to be able to race on your home tracks on the computer! I've used my computer to learn Mosport and Mont Tremblant before I ever went there, and to refresh my memory on Watkins Glen and Lime Rock.
Almost any recent computer will run the good racing sims, provided it has a good 3D video card. I'd go for the best you can afford, at least 1 Ghz and preferably in the 2 Ghz range.
For a video card, the best ones are GeForce Titanium or Ultra (the higher numbers, like 4, are better) and the later Raedeon Pro's.
You'll also need a controller. I prefer a ball-bearing equipped Logitech Wingman Formula Force (not GP!) These are no longer made but I've found them on eBay occasionally. I've converted a few to ball bearings, which is a pain, but really worth it.
The best currently available wheel is probably the Act Labs Force RS. The Logitech Momo Force (the one without the shift lever) is the best of the gear-driven wheels. At $140 it's a pretty good deal.
All of the above wheels come with pedals, but none of the pedals are very good. I use CH Pro Pedals, which work with any of the above wheels.
See http://www.logitech.com/, http://www.act-labs.com/, and http://www.chproducts.com/
Also see my GPL Survival Guide (in the Help section at http://alison.hine.net/gpl/) This has more info about hardware.
In my opinion, currently the best racing sims are:
Grand Prix Legends (aka GPL) - '67 Formula 1 season; Lotus 49, Dan Gurney's Eagle T1G, Ferrari 312, BRM H-16, more. Spa, Monaco, Silverstone, Zandvoort, Mosport, Monza, Watkins Glen, and an authentic version of the full 14 mile Nordschleife at the Nurburgring.
This is still my favorite, with wonderful cars, great tracks, very good physics, and excellent online racing.
Hundreds of tracks are available, including virtually every major track in the world and many club tracks. See the Links page on my GPL site for the GPL Track Database and GPL++ The Add-Ons.
Laguna Seca and Sears Point are both available for GPL, although you may need to jump through some hoops to get the non-NASCAR configuration of Sears Point. More info on the above sites and in the CART section of my GPL site.
Papyrus NASCAR Racing 2003 Season - The best physics - especially tires - available, and excellent online racing. Track converters are available to convert a number of the GPL tracks so you can run them with stock cars.
A Trans-Am mod is in the works. These cars should be a blast, especially on the road courses converted from GPL See http://theuspits.com/ and http://www.projectwildfire.com/ for more info.
EA Sports Formula 1 2002 and F1 Challenge - Decent physics, and F1C has good online multiplayer. A bunch of add-ons are available, but the best is the GTR 2002 add-on for F1 2002.
The developer, ISI, is about to release a new NASCAR sim, NASCAR Thunder 2004, which will be quite good and more readily extensible than Papyrus' NASCAR sim, so eventually there should be some great add-ons for it.
Others - Some non-commercial sims are highly thought of, including Live for Speed, Racer, and NetKar. However, these typically do not have a wide variety of real-world tracks available, which makes them of limited interest to me.
There's also an array of rally sims, but I haven't tried most of these, so I can't make any recommendations.
See the following sites for more info on racing sims: