A 110V MIG should be good. You can weld 3/16" - 1/8" thick material from one side in one pass depending on the welder you buy. If you can get to both sides of an item, you can weld almost twice the thickness stated. MIG welders are easier to learn to use and distort metal less.
What you call an "ARC" welder is really a "shielded metal arc welder" (SMAW), commonly called a "stick" welder. MIG, TIG, and SMAW and all forms of electric arc welding. The SMAW is great for heavy material, 1/8" and thicker. It's difficult (but not impossible) to weld thinner material. For thick metal you "drag" the torch, with the wire angled toward the weld that you just laid and as close to 90* over the joint as possible. Lean the torch 15-20* in the direction of travel. For thin material you "push" the torch in FRONT of the weld, angled 15-20* AWAY from the direction of travel. This lets the weld cool more and distorts the metal less. THE ANGLES ARE CRITICAL, especially the 90* over the work. It's hard to describe without pics, but if the angles aren't right, there will be to little or to much penetration.
With the MIG, if the material is over 1/8" or you can't get to both sides, just bevel the edges then weld. Leave a 3/16" flat where the two pieces come together, bevel above this. Leave a gap the thickness of the welding wire between the 3/16" flats to insure proper penetration.
Pick up the book that Home Depot and Lowe's sells on welding and read through it before you buy. That will give you a better idea of what you need and how to do it. After that it's just practice.
Oh yeah, I'm a basic welding instructor for the USAF.