I have a Gazelle. I use Make the cut instead of the software that came with the machine because I've been using MTC for a long time and didn't want to learn new software. The Gazelle came with a deep blade that will cut chipboard, not sure about cutting rubber stamp material, that's out of my wheel house.
I would suggest you consider trying out software first. I use Make the Cut, it cuts on all the major cutter brands (except Cricuts... unless you're grandfathered... which is a totally different discussion. MTC comes with free upgrades and is committed to working with any cutter company that will have them.
You can try Make-the-cut for free and get access to their boards. On their boards you will find many cutters (the good kind) and they will likely have the best advice. Off hand I *think* Black Cat or Klic-N-Kut will cut with the most pressure, thus the strongest materials, but I am not sure.