Yes, do be yourself, not put on any sort of mask of what you think a family with a nanny should be like. I tend to work with parents who are fairly laid back, easy going, non-formal, house a bit of a mess not spotless marble floors.
Talk about what you would like the children doing during the day. Some nannies love being at home all day doing arts and crafts and other things, whilst others will go stir crazy if not able to go out for a walk in the woods every day. Also think about what your children need... you may need someone who is very consistent, who sticks to routines, who does not panic when things do not go to plan but instead adapts quickly to the new situation.
Sometimes it simply comes down to whom your children respond to. Some of the children I have worked with have been on the autistic spectrum and I remember one non-verbal 4 year old who would not go near anyone other than close family, would not interact with anyone... but when I arrived for an interview he came charging over and jumped on my lap and sat there showing me his toy car. So sometimes it is the child who chooses!
In business you try to find someone who complements your skills, who fits in the team but brings more things to that team. With nannies, I feel you are looking for someone who is similar to you, who has the same approach to bringing up children. They may had addition skills and they may not agree 100% with the way you do things, but they will be 95% of the way there. Everyone will have their own views on this though, so you need to decide what sort of person you want to work with your family.
Are your children of an age where they can tell you who they like? Are they very shy around new people, so if you see them accepting a new person very quickly will that be clearly seen?