Great that you're a member of the SCBWI! Do you have a writer friend you could test out your pitch on?
I would prepare for it by writing out a bullet-list of the points you're aiming to cover and write out a short prepared pitch that you can go over (you don't have to memorise every word but it's good to have a plan to quell your nerves!) Something along the lines of:
Hello X, thanks for your time.
I'm writing a children's book aimed at xx-year-olds which will be approx. xx words when it's finished (this will demonstrate that you understand the general rules regarding age ranges and word counts and in answer to your question above, it's definitely a detail they will want to know).
It's a comedy-drama/contemporary/historical fiction/fantasy/thriller/coming of age tale about XX Character name.
Then follow up with two or three sentences summing up the story try and make it as punchy and exciting as possible. Try also to include a compelling detail about your protagonist what you want here is for the publisher to want to know more and to ask you a few questions about the story. Don't worry about them asking you something you don't know or haven't decided -- they understand what a WIP is and means. If you are passionate about your story it will show, and it will go a long way to making them want to read some of it.
Questions to prepare for:
Have you been writing long?
Is this your first manuscript?
How would you describe your style? (If you want to bring in some other author names make sure you say something like: 'I think it might appeal to the audience of xx and xx' rather than saying you are 'like' any one out there). You are different and they will want you to be different. Publishers are always on the search for someone new and fresh.
Think of it as a conversation rather than a ten-minute pitch (you're right, that would be a LONG pitch!)
Yes, I think it would be a good idea to be prepared to answer a question on what you have enjoyed reading recently. It's an industry based on passion so you need to show you are as passionate about reading books as you are about writing them. Make sure the titles are recent enough to demonstrate that you're aware of what's being published now.
Also, the publisher will ask questions but remember this is also your opportunity to ask questions of your own. Try and ask something that shows you know what's out there and are interested in current trends (though also remember that what you are seeing in shops was commissioned at least a year and often two years before sure you know this though!) Maybe ask if there is a particular genre/type of story that they prefer or aren't seeing enough of or just compliment a recent publication of theirs -- they'll appreciate it and it might make them more receptive!
Really hope some of the above is helpful. But even if it doesn't result in the outcome you're hoping for, please remember there will be lots of other opportunities out there. Once you have a good book in your hands, everything else will follow. The most important thing is making sure your book is as good and 'ready' as it can be before it goes out.
Wishing you lots of luck!