I would suggest you get your feet wet by doing some of the license tests, followed by some GT mode grip races. Once you have managed to save some credits (let's say anywhere from 50,000cr to 100,000cr), have a look at the Seasonal Races. Find one that interests you, go build a car that fits the required criteria, and then grind that race/races for a while. Save up half a million to a million credits, and you'll be set for the rest of your GT5 experience. Whenever you need cash, head back to the seasonals...they are by far the best way to make money quickly.
I would avoid trying to drift right away. Get a feel for the physics of the game by doing some grip racing. IMO, drifting is one of the most difficult activities to learn in gt5, as there is a very steep learning curve.
That said, when you think you are ready for drifting, head on over to the drift forums and introduce yourself. There's tons of advice and info for beginners, as well as lots of very friendly and helpful personalities.
My quick and dirty tips for getting into drifting are this:
1 - buy either a premium
Mazda FC3S RX7 GT-X or a premium
Nissan PS13 Silvia K's Dia Selection
2 - buy
comfort hard tires and a fully customizable LSD (limited slip differential). Leave all settings stock. Comfort hard tires are not a necessity for drifting, but if you wan to "fit in" with the GTP GT5 drift scene, and attend lobbies and competitions hosted by GTP members, comfort hard tires are a must.
3 - turn off all driver aids. You can leave ABS on if you like.
4 - go to Top Gear Test Track, the S-curve at High Speed Ring, or turn 1 at Deep Forest, and just start gettin' sideways
5 - remember, if you're not spinning out and crashing, you're not learning to drift

. Don't get frustrated and be patient...learning to drift doesn't happen over night. Most of us drifters will tell you the same thing...it takes a couple of months of practice to get halfways decent. I've been drifting for about a year and a half now, and am just now starting to feel completely confident in my abilities. And remember, KDF!!!
Welcome to GTP, hope to see you out on track one day