Lets get some info going on what people play, why and with what. Ill try to make it concise.
Setup: Fanatec GT3RS w/ Clubsport Pedals. Highly recommended, pedals and wheels are amazing, shifter is terrible, particularly the attachment. Single monitor, basic desktop computer and office chair.
Never been in a league but have been looking for one recently. Typically I like GT1/3-esque race cars, touring cars and some open wheelers.
Just let my Iracing expire. Great tool, not fun enough though and requires too much time. Also expensive. Great and most organized community, pretty great system to develop new drivers. Physics are hit/miss for me, on the general they are decent, there is definitely an element of them being artificially difficult. Particularly with cars sliding. Favorite car was the Mustang. Only racecars.
Live for Speed (LFS). Just tried this after 2 year absence. Don't know if it was the trial by fire of Iracing, but man is this game much more fun and easier to drive with slip angle. One time fee got me all the cars and tracks. The physics feel the most "right" to me in this game. Great but dwindling community, getting dated with updates being far and few in between. No real tracks or cars, but obvious car copies: You get your "porsche" car, Lotus 7s, Turbo 200hp RWD (944 turbo/FC turbo looking car), Turbo kit roadster, and some open wheelers. Awesome autocross editor lets you make your own courses.
Rfactor. Largest community, game is a bit of a bandaid hackjob because the game comes very basic originally but many mods are available. One time fee like LFS. Game experience depends entirely on mods, some are terrible, some are great. I personally have very little seat time but I am a fan of the Porsche Cup car mod. You can download pretty much anything you can think of for this game, question is whether it is accurate or well done. All tracks and cars are free. Probably will download the FSONE 2009 and the infamous cart mod. Largest supported racer, many leagues and racing of all kinds.
Dirt 3. Not very realistic (you go with Richard Burns Rally for the realism) but SO MUCH FUN. 600 hp group B flying around like mad? Yes please. It was cheap, and I found myself playing it much more than Iracing because it was fun. I would say this is on par with GT5 for realism except on dirt. Flashy, fast and fun.
F1-2011 Great looking, somewhere in between Gt5 and hardcore sim. Much more polish than a lot of the mod-sim racers. Not a very serious community. Fun to play through the story mode, this one wont keep you hooked like RFactor for 10 years.