Congratulations on your engagement.
Generally speaking, if you have overstayed your visa, and are married to a US citizen (and the marriage is not for the purpose of evading immigration laws, ie a "sham"), then the USCIS will "forgive" your status. You should always wait at least 60 days and even better 90+ days after your last entry to get married. Sounds like that isn't a problem.
Although people do obtain green cards by spouse sponsorship on their own, it is highly advisable to at least consult and immigration attorney, particularly when you have waiver issues such as being out of status. Best give a call to an immigration attorney and then take it from there.
For your second part of the question, for my clients the process is taking about 3.5 months to 4 months, but I am in CA where there is a different processing center and immigration office, so it might be a little different where you are. You can expect the process to take 4-7 months.
Best of luck!
This is not legal advice and is only general information. I am not your attorney. No attorney-client relationship is formed by this communication.
If your fiancee is a US citizen, the fact that you are now out of status will not be a problem. Generally, it takes about 3 to 6 months from filing to interview, assuming there was no delay in responding to a Request for Evidence, if any.
A lot will depend on the immigration status of your girlfriend.
The information contained in this answer is provided for informational purposes only, and should not be construed as legal advice on any subject matter,not should it be viewed as establishing an attorney client relationship of any kind.