Here is a video of my setup. http://youtu.be/MtoQil-EI0s (Please note that I made the video to show my brother my setup)
The matt was made out of high density foam puzzle tiles. The puzzle tiles are used for play rooms or exercise rooms. I found that by stacking them 2 high and placing a piece of carpet on top brought me to the perfect height. I used a razor knife to cut out a place for the swing pad. The nice thing about the puzzle squares is that they are very inexpensive and you can hook them together (the edges lock together like a puzzle) to make any size matt that you want.
The screen was made from a extra heavy duty tarp that I bought from Northern Tool. It is an extremely strong tarp rated at 1000 Denier. I laminated white vinyl (like what is used for seat covers) on top of the tarp with contact cement. The vinyl comes with a fuzzy backing or for the more expensive stuff, it is not fuzzy. I used more expensive type since I glued the shiny or top side of the vinyl to the tarp. The lamination process was a little tricky.
The screen ended up costing me under $150 to construct and it seems to be holding up well and to date have fired at least 1000 real balls into it.
I bought a net for about $40 but ended up cutting the net and the polls to customize my setup. I had to use some of the netting to make an "awning" at the top to stop balls from flying over top the screen when using wedges. I also rigged some netting on the right side to catch balls that were hit on the tow of the cub.