(Warning: This is long-winded.)
Hey Shock, a lot of folks have already made valid points... mainly about the torque-happy Viper being a bad choice for such a confined course like Cote d'Azur. Wheelspin is never helpful, but it's your worst enemy on twisty tracks. I dunno about the advice on buying an RX-7 though, it's not what I'd call ideal for a novice driver. A Silvia K's 2000cc or a Sprinter Trueno might be better, for learning purposes at least.
Anyway, to chip in my advice... use the Free Run mode for practice, and use it often. Complex String is a scary looking piece of asphalt, but it contains just about every kind of corner you'll come up against, so you might want to give that some time first, and then try the other tracks available to you to get familiar with them. After all, the best racing teams will practice and test a lot during and after the season, and since you have no limit to your testing time, it's only smart to take advantage of it.
Another very, very important thing is learning where the brake points are on the track so you can take the corners properly. If you keep an eye on your gear indicator, you'll notice the recommended gear (the little red number) flash when you come up close on a turn... that's the trick. When it starts flashing, you should start braking. It takes a bit of practice, but as you get to know the track and your car you can learn when to get on and off the brakes. Remember, brake, THEN turn. As you get better, you can experiment with "late braking" and see how far you can cut into those zones without screwing up the turn.
As for the tire problem, don't even bother wasting money on the softer ones. They wear out far too quickly, and a soft tire that's red handles far worse than a slick tire that's green. I'd say that medium-slick is a good choice to start with, as it'll help you to learn how to deal with the reduced grip. As time goes on, try working with the slick tires and see if you can adjust to those. The skill you gain from all that practice will benefit you as much as the time you save from having to pit less.
I may be new to GT3, but thankfully a lot of my GT1 and GT2 experience carries over so I actually have an clue about what I'm blathering on here.