We use Martelli Ergo 60mm rotary cutters for all our shop cutting. Much easier to use, easier to control, and thus more accurate cuts than the long-handled ones.
They'll use any blades, but the Martelli blades seem to last a LOT longer than any other blades we've seen. With daily use and a lot of cutting, we only change them once every 6 months to a year. I also like that they come in left and right hand versions, since we need one of each.
The only weak point on them is that you need to close the blade cover manually, and the spring that holds the blade cover closed comes off easily, but a little preventative maintenance with a needle-nosed pliers fixes that problem.
I really wouldn't use any others.
We haven't used the mats, so no opinion there.