The Hobart Handler 140 always gets good reviews for a beginner machine. For a given amperage, flux core is always going to be a hotter process than "MIG", so consider flux-core for better penetration with limited power. Practice, practice, practice!
What I've always done (since I'm just a hobbyist!) is get me some scraps and practice at the beginning of a project. Once the weld profile looks ok, weld as large 6' angle to another at 90 degrees. Do a weld and crank on it until it breaks. You want the BASE metal to deform/yield/fracture, not the weld.
I learned welding on a Ironman 210 with flux core. I've done a little mig, but for structural projects I still prefer flux-core. I also learned stick on a Miller Thunderbolt AC machine. I've since "upgraded" to a Lincoln Idealarc AC/DC.
As far as your condition, I think I would try to hammer that back so the surface across is pretty close to being flush. Grind both sides. Tack a 3/16 plate on the bottom to act as a backing plate and try to do the weld from the top surface. Remove backing plate, and if necessary do another pass in the underside.
Good luck!