Ruler: My newest best friend is a 2.5 x 6.5 creative grid ruler, I love it and use it most by my machine.
Mats: I use Fiskars most because the colors enable me to see the edge of the fabric more clearly. I recently purchased the pink one which works great for the more intense jewel and earth tones I love. For the lighter colors I still use the OLFA green one. I also use a OLFA 5.5 x 7.5 and a Omnigrid 8 x 11 (these are actual grid measurements) on a table by my sewing chair for quick cuts.
Regarding mats and self-healing. I do not believe any of them are totally self-healing forever. If you always cut in the same area, you will lose that area. The trick for me is to use enough pressure to cut the fabric, but not so much that I cut deep into the mat.
Where are you visiting in the U.S.?