Just bought PC2 as well and I have to say that first impressions are very good! A big issue for me in GTS was playing solo against the AI which is just dreadful. Also not having Monaco or the old Hockenheim layout were little things I missed.
Any suggestions for someone that hasn't even started the career mode?
A few things off the top of my head which knowing me turned into a super-long post:
-Don't feel like you have to rush the career until you're somewhat used to the game. It doesn't really have an "easy mode" at the start, just the cars are slower. But there's no reason not to start it. You can always do some other races whenever you like(and you'll want to change things up now and then). The Ginetta Jr is a very forgiving car to start with and more fun than you might think 110mph can be. Some people have trouble making it turn at all but learning how much brake you can use will take you far in this one. The Formula Rookie is a bit more tricky but can teach you some different things.
-If you plan to race karts, keep in mind that there is no practice in career(because no pits) so you'll want to learn to drive them on your own first or you'll be restarting a lot. I don't think they are that difficult with some practice but they are quite different from everything else(and the FFB is wild on them, yes). They also have a few really difficult rain races - puddles seem a lot deeper when your tires are 4 inches high. Every other series I've done has a practice session(except some of the Invitationals).
-Speaking of restarts, don't worry about those stats. There's too many silly things that will happen to take them seriously. Even quitting at the start of qualifying to change difficulty goes on your record, although I'm pretty sure quitting before starting a race does not(not sure about during the formation lap).
-Get used to driving in the wet(with puddles) as you'll do it a lot. Get used to warming up your tires including in cool early spring / late fall weather because it is very important(and in some cars you have to drive pretty hard to get them to where you can start to feel comfortable). Plenty of championships will start early March or late February and end in November so there will be some chilly days.
-Most series at least in the first half of the career(what I've done... it's long if you drive everything) don't have the same driver up front every race so it's not like the fake-ish championships in some other games where you basically have to win every single event. You can make up lots of ground, but of course there's no guarantee and most championships aren't super long - usually 5 races.
-Don't be too attached to a number for AI difficulty. It can vary widely car-to-car and track-to-track, and what is good for the dry may not be good for the wet. In general you can expect the AI to be much faster in qualifying(1-2 seconds) and the race than in practice, but that does not always hold true as their pace can vary quite a lot at the same setting. They also tend in practice and qualifying to run some quick laps early and then drive more relaxed the rest of the session so don't let that fool you.
-There's no easy way to skip around and run championships you missed or re-run your favorites, so you'll want to do all the ones you want in one tier before moving up(you can only go up or down one tier at the end of the year).
Like Beezer215 said, just pick what you like and do it, there's not really any problems you can get stuck on. Most of what you'll need to learn for the career... you can learn in the career. Worst case you'll have to retire from the races to quickly skip through a season you don't want to finish. People here are plenty willing to help if you have questions.