I the rotary cutter that has a shape blade. I have all 3 sizes of Olfa and use the 45mm most. I also have I think it fiskers (gray and orange with ego handle). I use that a lot too.
You are not suppose to use your mat to measure your strip is they need to be acurate. I cut out a king size quilt using my mat to measure and it was a mess. If you need to cut a strip large than you 24" ruler, place your cut edge on the right (for righties) and then use your square up on the cut edge to measure the width of your strip. Put your 24" against the square-up and move square up away enough to cut the strip.
I have a shape cutter and would love it more if it went to 12 1/2". I know there is a bigger one but I don't own it. Elenor Burns (I think it is hers, she uses it) has one that only cuts 2 1/2" strips I would love to have one of those.
Before you buy a mat, think about what color you cut most and don't buy a mat that color. I have a blue mat that I never use because most of my fabric is blue and it make it hard to see the edge of your fabric. In my studio I have the big mat (36X60")from JoAnns that goes on craft table they sell. I bought a hollow core door and 4 adjustable legs from Ikea to make a cutting talbe. I added molding around the edge (sticking up just enough to hold mat in place). I bought a piece of hard wood that was 8" X36" and had a friend of mine router groves the length for all my rulers (or at least most). This is a one end the mat comes next and I still have a small area at the end without any mat that I can stack whatever.