To the OP:
Congrats on deciding to get married!

We're here to help you and provide you with information. It's up to you as to the path you take.
I posted this in another topic, but I feel it is relevant.
"The USCIS sees cases where a person enters on a visitor visa, spontaneously decides to marry (although spontaneous is rather...subjective...in some cases, and it really is up to the petitioner to prove spontaneity in the decision to marry.), and adjusts status within the USA. When we talked to a USCIS officer, she said "alot of people get away with that" meaning that the process I described above is not exactly legal, but the USCIS has some discretion for these particular cases."
You will need to get married before you file paperwork. And, be aware of both the cost to file and the time it takes before you can work and leave the US. You may want to check current timelines for Employment Authorization (EAD) and Advance Parole (AP) before you decide to stay. Last time I checked, it was about 60-90 days before you got EAD and/or AP. I'm not sure if you are aware of this, but if you are filing for AOS and need to leave the country before you get AP, then that has serious consequences ranging from not being allowed back in to the US to the USCIS considering the AOS application 'abandoned' because you left the US.
On a side note: I live in a liberal town, where the use of "partner" incorporates heterosexual and homosexual relationships. I noticed you said "partner" in your original post. Please note that the USCIS only recognizes marriages between a man and a woman, even if homosexual civil unions and/or marriages are legal in your country.