It really is up to you mate, but here's a few tips that might help you make a decision on the direction you take:
1. Online is really the meat of GT5, making money and having fun races are best done this way. If you want to make lots of credits fast the 'Seasonal Events' you will find on the left of your career screen is your best especially the newest one with the Corvette C7 as you get gifted the car I do believe but don't even need to own one I don't think.
Seasonal Events Usually don't require you to be a specific driver level but the car you may need might be a higher level than you think so keep that in mind until you get to around level 20(which is easily achieved in the Seasonals). You also can do the Time Trial and Drift Trial ones which change monthly I think for some fairly easy rewards and credits.
2. If you want to develop your skills in all of GT5's different categories of racing go for the 'Special Event' tests, they are fun and give you an idea of most of the types of racing you can do in GT5. Some of them are incredibly fun, some very frustrating but you learn from them.
3. Once you have got some credits and cars you can either choose to start going online to meet other racers though you might want to meet some here to get you into some clean rooms online, or if you already have friends online on ps3 you can join them. Keep in mind if you have never been online that there a hundreds of thousands of other people and not all rooms are good choices. But have fun, build your levels up in Aspec so if you join good rooms people know you have some ability to keep the car on the blacktop and then GT5 online is really your oyster. Check out the many parts of GTP as it has helped me tremendously in a very short time.
4. Cars need to be ran over 300km/180miles to be 'run in' and get full power, so if a car has less than that mileage it is not at max power yet. Once the car has this much mileage you need to generally do the engine and chassis rebuild in the servicing section of GT5. This does not apply to the cars you can buy from the 'Online Car Dealership' and I highly recommend that if you have the credits and you want a certain car from there you buy it as the cars change usually at the same time as the seasonal events. Cars with full power are slightly faster overall.