I would just keep at it online. As long as you find the right places to race with people who are close to your speed you will improve and have fun. Try and avoid the servers that are too messy
You can join leagues, you just need to find the right one for yourself. Have look in the leagues section :P There should be a few open events you can hop into.
Career path.....hmmm........just race and practice, rinse and repeat
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For me, practicing offline on my own is no fun, so in order to progress just keep racing online and that way you can gauge your progress too. Hot-lapping helps some people, but it isnt my cup of tea.