Fair rent amount for girlfriend moving in with me in the home I own?

Hello. I (32m) own my home and have a mortgage of $1140 per month. I live with my mentally challenged brother who gets SSI for disability, and my brother pays me $300 a month for a room in my house. My girlfriend and I have been together over a year, but living separately. We've started talking about moving in together, but are at somewhat of a standstill on the amount of dollars per month she would pay me in 'rent.'

We both work full time jobs, and her car is paid off. She lives with her parents and is eager to move out. My car is not paid off, if that matters. Anyway, we have come up with three possible arrangements when it comes to her "chipping in."

1) Her proposal, my brother pays $300 monthly and gets a whole bedroom. She will be getting "half of the master bedroom," and thus should pay half what my brother pays: $150 a month.

2) My proposal, we are partners and we should do things 50/50. My brothers disability income is quite limited, and I think $300 a month is fair for him and should remain unchanged. We should split the remainder evenly between us: $420 a month.

3) Compromise, she the same amount as my brother. Since I am the sole owner of the house, I have the most to gain when/if I sell the house. She wants a "girlfriend discount," and this maybe possibly is a way to provide that: $300 a month.

I made the point that $300 a month is far cheaper than she could ever live anywhere else, and she said I was making a sales pitch. I just want an arrangement that is fair, and doesn't have me cheating her out hard earned money. I apologize if this Subreddit is not the right one for this, I'm just trying to solicit the advice of strangers to help clear my head and allow us both to be happy.