You should want to keep things new and interesting, as you would in any relationship, while still allowing your date to maintain the standards of her faith. Which is an absolute lie.
This is tough enough when the kids are babies, but when they're older - teenagers - you'll get to tackle all of the hormone-fueled angst, drama, school difficulties, homework, school activities, and be the scapegoat when the kids get mad at you. I am dating a great guy who happens to be a very brilliant doctor going into residency very soon.
I have a 12 year old daughter from my first marriage and so we didn't move in with him until he and I had been together for 2 years.