Use 1/4"

I used 3/16 in a few places over the years on various parts of "version ones" of my welding projects, and it's proving to be not strong enough.

You might want to consider extending some of the plates so that they can transfer weight to the full width of the cross-members, not just onto the edges. I've pulled a few factory bolt holes using them to take all the weight that the skids can transfer.

Make cardboard templates to test fit, and take a good look at where the stresses will go when the plate's loaded. Make sure to increase the stress-transfer overlap regions.