F1 marrying US citizen

[Northes 0]

I'm an Australian citizen, attending grad school in the US on an F-1 visa. My fiance is a US citizen (born in the US) and we have been cohabiting for six years. I'm thinking about leaving my PhD program at the end of this academic year (May 2015) but staying with him in the US. How would I go about adjusting my immigration status, and most importantly, how quickly should we get married and start the process? We would like to give our relatives time to coordinate travel plans so they can attend our wedding, even though it will only be a small ceremony, but obviously my priority is not finding myself out of status.

Also... I goofed and have not filed my taxes in about five years. The years before that when I did file my taxes, I was an undergrad only earning a small amount in the US as a student worker and either received or owed up to $50. Even now my grad student stipend is only about $18,000 before tax. I know it's something that I need to sort out eventually, and if there are penalties they will be minor, but is there any reason this would affect my application?

[Penguin_ie 5,999]

It would be better if you got married before you lost status, so before May. You could always get legeally married now, and then have a ceremony/reception later.

You can backfile your taxes, once done, it should not affect your application.