maz duh
+1y
.125 wall is plenty thick for a notch made of 2x3 tubing, you will get good well penitration even if you are using a 110v mig. The 3/16 you have chosen will work fine too, just a little more beef to it. Be sure to bevel your edges back at the mitre joints when you weld it up and you will be gold. Have fun building and be sure to show us some pix when your done.