Cecilia:
Thanks for asking the opinion of the Mom's Panel for your first Disney vacation! I feel so honored!
With a 3-year-old and another toddler, I think the Value and Moderate resorts are good choices. The smaller rooms are accommodating, the pools don't have to be over-the-top, and the price allows you to save money you can spend on a few Character Meals!
My two recommendations in this category, considering the ages of your children, would be
Caribbean Beach Resort and All-Star Movies. Although
Port Orleans: French Quarter offers the boat to Downtown Disney, Caribbean Beach Resort features more that may appeal to toddlers and preschoolers, including several playgrounds around the resort along with a newly renovated kiddie pool with a pirate ship water feature, not to mention white sand beaches. Its standard rooms are Nemo-themed while its preferred rooms sport a pirate theme!
If you're on a budget, my children still remember their stay at All-Star Movies six years ago! We stayed in the Toy Story buildings and the three-story tall Buzz Lightyear was quite a photo op! It may be more interesting to your 3-year-old than, say, a big wheel at Pop Century.....the rooms are the same size at both resorts, so I'd choose it simply based on theming.
If you're planning on staying at least a day or so at your resort, go for Caribbean Beach Resort. If you want a resort that you can enjoy as well the kids, French Quarter's boat gives it a leg up....
Wishing y'all a magical vacation!
Whitney