While it used to be an option to start participating in national politics in a substantive way, currently you have to wait for party leadership to put you on their list for next election. But if you're interested in that sort of thing, I think you should jump right in in your new province. I'm not currently sure whether or not you can get a seat in the assembly, but if you can't, then I will work on changing a lot so that you can (EDIT: see the M-M board -- working on it now)! and you can still join a political party if you're so inclined on the national level. There are currently three active ones, although I will let the various politicians who represent them speak for themselves.
Beyond that, there is a media organization, a news magazine published by Ian P. You can read some of those back issues and even write for it yourself, since he's very glad to print submissions.
If you wanted to request a coat of arms for yourself, that's also an option and something interesting a lot of new citizens like to do.
There has previously been a branch of the military devoted to cultural service that could have guided you, but it is not active right now. That might change soon though, hopefully.
There is also the national wiki, where you can request an account and start contributing. If you're not sure about how to edit a wiki, there is a tutorial that I made available specific to our own.
EDIT: Made this less Debbie Downer.