I'm "new school" and have gone to the "old school" of haul-it in the stool. Used to have a homemade cart (axle, wheels and handle on my shooting stool), but if that didn't get to be a bit of a burden at times on the range. Now I toss everything in my shooting stool, use my pit rope for a shoulder strap and carry the rifle case, mat and scope down the line that way. Oh, and when I get out for longer matches, I like a small daypack to carry my water and feed bag. (I'm young, skinny and have been accused of having the metabolism of a 140-lb shrew!
But there are many way to improvise a shooting cart out of your stool. Take a look at some of the set-ups on the line and ask questions of the builders.