I cannot speak from the adult's perspective, but I can from the child's perspective (sort of). My father passed when I was 11 and my mom began dating when I was 17 (my little sis was 14). She only dated one man and did marry him. At first he was over for dinner every night and would stay until 8pm or so. It was TOO much! After many tears and discussions, he came over less frequently. They eventually became engaged, but decided not to get married until my little sister graduated high school and left for college. He did not sleep over or move in until my sister left for college.
You are a parent first! I realize waiting until your daughter leaves for college is an awful long time, but you need to take things slow. Does he have full custody of his kids? His kids are a lot older than your daughter and are going to deal with it very differently. They are probably very protective of your daughter.
If you are very serious and think you will marry this man, please seek family counseling--especially for his kids. Counseling doesn't mean there is something wrong, but it can help guide you through uncharted waters.
Finally, always put the kids first. My mom has four kids (39, 36, 32, 29) and 8 grandchildren and we still come first--and her husband knows it.