Having an air compressor on a car is really a good thing for when going out for spudding in the woods. I should look into that.
And a welder?! Wtf! Its really awesome, but still, I dont really see why one needs a mobile welder. If you need to weld in a certain project, do it in your workshop. Maybe emergency repairs for something, but I have never felt the need for that.
What size of spudgun would you keep in your vehicle for those time you need to relax and shoot a tater into the stratosphere? 
You mean a gun to go out spudding with every now and then or a gun that's permanently in your car so you can launch a random unlucky object wherever you are?
For the first one, as big as fits.
For the second one, as big as it fits without going diagonally through your car. Just flat in the trunk.
Maybe use some sort of system to unscrew your barrel in shorter pieces.
Or make a small one running on high pressure. But you will need a proper air source for that too; maybe a fridge compressor.