Well, it doesn't sound like you're considering marriage, just cohabiting. Which is what My Lady and I are doing.
We were in an LDR (long-distance relationship) for 4 years before I got a job in her city. Early on, we decided one of us would have to move, and it ended up being me.
We had the big items discussed in advance. I was moving into her house. It is not my house. It is her primary asset owned free-and-clear, and she wants to preserve it. I calculated what I thought was a fair amount to pay each month for household expenses such as groceries, utilities, cable, internet, etc. and she concurred.
Once we got over the hurdles of moving in and her 2 boys adjusting to my presence, and sharing a bathroom and a morning schedule, I came to realize that I probably guessed low on that amount. So I now also buy all the weekly groceries and fill up her gas tank often.
So I think you need to figure out what he needs to contribute, and be open to changing that idea later on when actual experience differs from your plan.
There are also considerations about cooking, cleaning, errands, chores, and... parenting. My kids were grown and mostly independent, and My Lady's kids were college age. Their father lives not-too-far away, and while I serve a function as another adult in the house, I am not their father and don't pretend to be. What's his relationship with your kids going to be after he moves in?
Another consideration is unintentionally committing common-law marriage. You need to check out the laws in your state. When I had my will made out, I asked my attorney about that, and he explained the guidelines in Texas.
As I recall, (and this is not legal advice), in Texas you need some number of the following:
1. Presenting in public as married.
2. Commingling money and bank accounts.
3. Owning real estate together.