Like Jilly, I was about to say check out the step-parenting board - there are some general threads on there, where people say what works well and what doesn't, as well as lots of specific problem ones. I'd say it should be required reading for anyone who is embarking on a relationship with a parent!
From my point of view, my DP has 2 DCs and while they are lovely kids, it is difficult knowing you will never come first to your partner, which can cause some resentment. He does his best to spend as much time with me as possible, but it is tricky when he goes away on business and I have missed him so much, but then he has to rush off to see his DCs who have also missed him, so his visit to me is usually first --as he leaves his car here- but fleeting!
There have been times where he was with me but wouldn't say so when he spoke to them as they'd be jealous, which made me feel a bit like an OW!
Their mum is very nice, not really my sort of person, but she's never given me any trouble. However, she is a constant factor in his life, calling and texting at inappropriate times, which can cause friction. In the early days she did get a bit jealous about her DCs staying here with us, but DP put her straight and told her that she didn't have any say in what happened when they were with him.
On that note, any problems with the ex are up to your DP to sort out, you need to take a step back from it all, don't get involved in any of their issues and make sure she knows you're not trying to tread on her toes. As long as you and your DP are on the same page you will be fine.
I would also say, be careful to allow him and his DD time on their own together as she will no doubt love you, but also be jealous that you get to spend time with her dad when she doesn't. Even more so if you have DCs of your own. Giving her time with her dad will help her to feel special to him.
My DCs' dad has a GF and they all really like her. It is strange knowing that they all have this loving relationship with someone I don't know at all, but I'm unusual in that I don't feel jealous at all when DD says she loves her dad's GF or writes letters to her etc. I see her like a lovely aunty, she won't ever be mum, she's just someone else that DD loves.