I would try some 3/32" or 1/8" 6013 for your project. The clamps should weld decently and the "buzz box" you have will run 6013 with no problems, and give a smooth looking weld.
I would remove the paint from the welding zones before welding. Allow the clamps to cool slowly, don't dunk them in water.
7018 electrodes would also work well but you will probably have some difficulties running them with your Lincoln machine.
I would not weld the clamps if you have a critical application for them, like anchors for bungee jumping or anything else that would put life or property in jeopardy if the welds fail. But the application you have described should be no problem.
Chet Guilford