The advice given by others to research is absolutely sound.
The cheapest way to stay in a Value or Moderate Disney resort is almost always to book room-only with a Disney percent-off discount, plus any stackable discounts you can get. Currently Orbitz/Cheaptickets have been running the best stackable discounts. By next year, that could change. The same basic advice applies to Deluxe resorts, but you should first look at the Deluxe Villa (DVC) resorts because you often get almost identical rooms and benefits for less money via renting DVC points. Well, the cheapest over the long term is to buy into DVC, but that's a much larger commitment and isn't particularly cheap in terms of up front costs.
Renting DVC points to stay in Studios is a great savings, but be aware that there are some differences with staying on a cash reservation. DVC Studios don't usually have two beds; they have a Queen bed and a Full pull-out sofa (and a pull-out or pull-down single bed in some units). You also don't get daily housekeeping when staying on points. And typically the cancellation policy when renting points is very inflexible. Getting third-party trip cancellation insurance is a good idea.
Booking with a TA is not primarily about savings, it's about getting superior service, though many people do save money with a TA via the TA finding them deals they didn't know about, or using various booking tricks to get equivalent accommodations which cost the client less. It's more about knowing the system and being able to work the angles. People who know Disney inside and out may pooh-pooh these kinds of advantages, but TAs can really do amazing things sometimes, like find ways to book a room with a discount that's showing as having no discounted rooms available. Knowledge is power, and a great TA has a lot of knowledge. If you're a "go it alone" kind of person, though, a TA might not be the right choice.