Congratulations!
A couple of initial tips, but you will find many, many items that will be helpful by just reading the various posts and/or trip reports on Disboards.
First of all, you say you are going in April 2009 for the first time. Please realize that Easter falls on April 12th. Typically the weeks wrapping Easter are PACKED! That would be the week of April 5th and Easter week (week of April 12th). Additionally, based on past experience, I think you will find it pretty busy the week of March 29th as well. I always feel bad for anyone taking their family for a first visit during such a busy time. It is do-able but you really need to take advantage of the EMH, fastpasses, etc. that are offered.
If you can go the week of April 19th or the 26th you may find things much better re the crowds.
Okay, another key piece of advice I would offer at this initial stage is to plan on being their a minimum of 6-7 nights. It is better if you can go for longer, but for a first visit during a busy time, I would say a MINIMUM of 6-7 nights. Especially with children, you will need to take those breaks from the park. The weather will be nice and they will definitely want to swim and you will need the break as well.
Other than the above, I'd say purchase the Unofficial Guide to WDW and read it cover-to-cover and also, get your room reserved as soon as you can. Any codes are discounts can be added later, but you do want to lock in your hotel room.
Again, you'll have a great time BUT can't stress enough the planning ... things/weather will happen and you'll want to be flexible, but you'll be glad that you have Plan A, Plan B, Plan C up your sleeve!
and congrats!!! 
and 
