Depends on what you are looking for.
If you just want a sturdy frame, but don't care how it looks, you could just use pine. Pine is less costly than most other woods, and is what most 2x4s are made from (that you can readily buy at the local hardware superstore).
If you care a little bit about looks, then you can still build the frame from pine, but then use another wood that has a better appearance (such as oak, cherry, etc).
If you want to build a family heirloom, then you can probably build the whole thing from wood with a better appearance (such as oak, cherry, etc), but it will cost you an arm and a leg.
Hope that helps.