I usually use the same size backer board and make it out of 1/8 plywood. Any thicker and you will have a hard time fitting it in a standard frame. I spray paint my backer with a flat black finish. As mrsn said many people use felt or card stock, which you can buy at any craft shop, these give you more variety of color.
I use Arlene's tacky glue. It is clear, and it also dries clear, which helps the glue not to show. I don't use glass. I take the glass out for two reasons. I don't like the glare and it keeps the piece thin enough to fit well in the frame.
This may be too obvious
, but I use good plywood for my piece (baltic birch) and the cheap stuff for the backer. I usually watch for sales or make my own frames. But I have had pieces that I had professionally framed. This depends on how nice the piece is or to who(m?) I am trying to impress.
Barry