There's lots of good advice here, but I see lots of expensive advice too.
My "budget" advice would be this:
Disney's All-Star Resorts are great, inexpensive, and you get the same Disney service that you get at any of the other Disney Resort hotels.
There is Disney transportation offered for free from the airport to ANY of the Disney hotels, and it is free and easy.
There are Disney resort busses that go from EACH resort to EACH Disney park and Downtown Disney, so don't worry about the ease of getting around. You will do fine.
The parks are great, but every time we have gone, we have done one park for the visit, and the rest of the time is spent swimming, exploring, relaxing, visiting Downtown Disney, etc.
A couple of our favorite free or cheap things to do:
1. At Fort Wilderness resort, there is a nightly FREE character meet and greet at the Campfire. You can buy the stuff to do Smores (or just bring your own in a little cooler), and Chip and Dale come out and take pics with each child. Plus they play a movie as it gets dark. We have gone every year and there has never been a crowd. Its the best kept secret on the Property! You would just find out the time for the Fort Wilderness Campfire movie, take a bus from your resort to Magic Kingdom, then get once at the gates to MK, you get on the bus going to Fort Wilderness. It's pretty easy, and the bussing will take about 30 min total. You reverse that to get back to your resort.
We love going to Downtown Disney to take in the sights and sounds. There is a Rainforest Cafe that is really fun to eat at, and a great ice cream place is down there too.
If you take a bus to the Baordwalk Resort in the evening, you can walk the boardwalk, and head over toward the bridge to Epcot, and watch Epcot's fireworks show right from the bridge! Its beautiful!
You can take a bus to MK, and then get on the ferry to wherever you want to go, even if its just the 40 minute round-trip around the lagoon. Its free.
Same thing with the monorail. Hop on at MK, and take it the full way around or get off at each of the resorts to look around at the amazing hotels (you can go inside, browse the gift shops, walk the grounds by the pools, eat outside by the pools, and at some, even swim).
We have always had great luck going to "visit" Animal Kingdom Lodge. It is a breath-taking resort. There are animals on the savannah that you can go visit, the pool is amazing ( and we always where our suits and take a beach bag with towels to take a dip-never had anyone say a word to us) and then we usually stay and eat lunch at the "quick-eats" restaurant they have by the pool. You can go inside, pick your food (if you do the Disney dining plan, it works there too), and then take your meal outdoors and eat at the tables that are right by the pool. Its a lovely way to spend a day.
We always do these fun and free things and end up having a wonderful time. Check out Mousesavers.com. There are really good tips there for budget ideas too!