My first piece of advice is that you should be asking your girlfriend this question, not a bunch of strangers on the internet.
That said, here's how I have structured this in my own life. (I've been in this situation twice and handled it differently each time, depending on everybody's needs and thought processes at the time.
The first time, his house remained 100% his. I agreed before moving in that I would have no equity in the property nor any claim to it. With that, I refused to pay one dime towards his mortgage nor did I pay anything towards utilities. Instead, I paid for 100% of all other "joint" expenses, such as groceries, car insurance (but not his car payment), dining out, vacations, etc. This came out to roughly 50/50 most of the time and we did not sweat the details.
We actually crafted our own "pre-nup" for this that we both signed and agreed to. When we split up many years later, it was a pretty easy process due to going into the scenario with eyes wide open. Expectations were set perfectly on both parts way in advance.
The second time, we agreed that I would pay a specific monthly amount which would go towards "my" portion of utilities and groceries. I agreed that I would have no equity in the house. All other expenses remain separate - car insurance, health care, clothing, etc. Anything that needed to be purchased for the house (furniture, repairs, etc) were to be his expense. We take turns paying for eating out and anything else we do together.
Again, I signed a document agreeing that I would have no equity in the house. (It was my idea both times, by the way).
Sit down, talk things through with your girlfriend BEFORE you move in together. It's not romantic and it's not fun and there may be some hurt feelings on both sides, but in my opinion, hammering out these kinds of things is absolutely crucial before you make that kind of commitment. And if you can't resolve this topic, then the topic actually ends up taking care of itself. You will both find out where your limits are if/when ultimatums get issued.