I didnt go online but a few times early in the game... i spent my time in the beginning like I did back in GT1 and each other version of GT... I got as far through the licenses as I felt like before I got bored (I think it was I-B where I stopped in day 1 with a mix of gold silver and bronze complete and some I-A....) then I started moving through the A-Spec levels...
BUT The great thing about GT is its YOUR choice to get what YOU want out of the game... I am 95% complete with the offline game, own 830+ cars, have all silvers at least in all licenses I-B and less (with several golds in there) completed most Events, finished every seasonal event (except drift trials, not my thing... I have done a few, and for me they make a fun break)... B-Spec I have all races done and A-Spec I have half endurance races (you get those unlocked later in the game) and I am a level 34 A-Spec and I think 28-30 (its been a while) in B-Spec.
Basically sometimes I set goals that I want to all gold licenses... I will do that til bored... my new kick is all cars.... next, who knows... some do all paints, all gear, all tickets, 0/0/0 cars... and still others want #1 Time Trial in seasonal... Its whatever you make it to be...
Have fun and enjoy the experience... it never ends**
** I have played GT over 10 years now starting with GT1 on the PS1 all the way through including GT5 Prologue and now GT5... at least 95% complete on all (working on that some now on GT5)