2x4's split in half with a table saw is the way to go for the frame, if it's free standing then you can do 2x3's. The reason to get the 2x4 split instead of buying 2x2's is because the cut side will be flat and lie very nicely against the board, and actual cut size will be 1/4 of an inch bigger than 2x2 making it a little stronger. Also it'll be easier to find straight nice pieces of 2x4 as opposed to 2x2. (Lowe's near lakewood actually makes thousands of split 2x4's before sukkos)
For the actual panel use Luan, or 1/4 plywood for a little more sturdiness.
Make sure to glue the panel down to the side beams together with screws to prevent warping.
To make a nice strong sukka does take a lot of work. May come out more worth it to just buy a made one. Tellim in Lakewood makes some really nice ones for a fair price. (don't have any more details)
Keep in mind that even if you buy one you must take the time to buy some waterproofing to paint the boards with, otherwise they will warp very quickly and not last.