Welcome! My tips...
after dealing with the hassle of staying off-site with our son on our last visit (wasn't my idea), I highly recommend staying on-site, if you can afford it. The moderates are very nice and come with a free coffee maker and refrigerator. And the value-priced hotels are quite reasonably priced when compared to other hotels.
If you will have a car at Disney World, there may be days/times when you would find it easier to drive to the park rather than take the bus -- parking is free if you stay on-site. IMO, it's well worth paying the $ for parking, if you stay off-site.
We always take our own bottled water, juice boxes, and a few snacks. Though security checks all of the bags, I've never had a problem taking these items in to the parks -- I can buy a case of large bottled water for the price of two small bottles at Disney World.
Take it easy with the parks -- try not to over-schedule your trip. Check out the Disney World planning books at your local library. Before your visit, know what rides and attractions are age/height appropriate for your kids.
Take a break in the afternoon. When we had just our son, I would take him back for a nap while my husband rode the rollercoasters and such. Now that we have two young children, we plan to head back to the hotel for a nap for the baby and me while DH and DS play in the pool. This is unlikely to be the last time you ever go to DW, so don't feel like you have to do absolutely everything.
If you find yourself stuck at the park with a child that needs a nap or quiet time, find someplace quiet and out of the way and take a break. I highly recommend the monorail at MK as a great nap-taking destination.
Some experiences I enjoy doing with the kids: having at least one character meal and getting their silouettes done at the little store on Main Street in Magic Kingdom.
Since your children aren't in school yet, definitely go at some point when school is in session -- I like fall and winter for the low crowds. Plus, hotel prices are lower. Check prices for your trip as a package and a la carte. Be aware that DW sometimes offers room discounts to
AAA members (more than pays for the AAA card) and to Annual Pass holders (may be worth it if you plan to go again within the year).
Order the free planning video from
http://www.disneyworld.com and check out this site and
http://www.mousesavers.com and
http://www.allearsnet.com for great information that will help you to be prepared.
Good Luck,
EthansMom (and now Molly's too)