I think the DTM cars are the most fun way to learn the ring. They are fast enough to be exciting, and handle well enough that you can make big mistakes and not end up in the wall.
Rather than grinding Indy like everyone else seems to want to do all day (aside from the times that they take a break to come on here and whine about grinding indy

), try using the german touring car nordschleiffe race as your money-maker for a while. The ai is so pitiful that it is basically just a time trial that pays you for every lap.
Once you learn how the ai behaves in the first 2 turns, they wont affect your lap times significantly, so you can create benchmark times for the race to see how you're progressing. It's somewhere between 10-15 seconds longer than a time trial lap, for comparison. As a baseline for your total race time (soft tires, no hp mods (except oil change), no driving aids (that includes abs =0)), I would suggest that when you are consistently finishing the race in :
< 7:00 = you are getting the hang of it
< 6:55 = you know the track well
< 6:50 = now you're having a lot of fun (this is the time zone I generally finish in)
< 6:45 = this is a lap that would normally end up in the above category, except this time you drove well, and only made one or two stupid mistakes

< 6:40 = you are on the edge for the brunt of the lap and narrowly escape disaster more than once (I dont think I've ever finished the race in this bracket with these settings).
Once you get to know the ring, you will love it. Now that Ive golded all the licenses and special events, I spend the majority of my time doing different races on the ring.
Once you feel comfortable with this one then you can move up a notch or two and start doing the GT All Stars race to practice driving the Ring in group c cars. Your first few times trying to get the 787B around the track cleanly with no traction control and no abs will have you ready to throw the game disc out of a moving vehicle, but once you can do it consistently, you wont want to use the other cars in your garage