I think it's a very positive sign that you're thinking about how to get to know his children in advance of the first meeting. Now, because his children are quite young, this shouldn't be nearly as difficult as meeting, say, a teenager. So you can start by relaxing a bit. The key to the first meeting is being yourself. Drop the expectations of being their friend.
Friendships take time to develop.
Instead, just spend the day paying attention to, and caring for, these children. A small gift for each is appropriate, but don't go too elaborate, because it will look like you're trying to win their affection. Plan a day at the zoo, or reading hour at the library, or head over to their favorite playground. If the weather's bad, look in your local newspaper for ideas on what to do with little ones. All four of you should spend the day together, but be sure not to be too outwardly affectionate with their dad.