I am a self taught, hobby welder, so the value of my observations and suggestions is limited. That's not a bad looking weld IMO, there is a lack of penetration at the lower end of the weld; but there is a fine line between between getting good penetration and burning through with thin sheet metal. I wonder what that weld looks like on the other side:
A butt joint on thin sheet metal can be tough. If your controls are turned all the way down on your unit, suggestions above all sound good to me, i.e. weld in sections, let the metal cool. You might consider a metal table which will conduct away a little heat and reduce the risk of smoke and fire.
Here's a cheap TIG unit. I have one, an am happy with it.
Note that it lacks AC so won't do Aluminum, it can do DC+ and DC- by switching the cables. The powersupply autoswitches between 110 and 220 so you can plug it in to a household outlet for convenience and into 220 when you've got it.
It does Stick, TIG, and plasma cutting. Made in China and sold on the Gianttech website and on eBay. I picked mine up for less than $500.
After having used Stick and MIG machines in the past, TIG is kind of fun, lots of control. The plasma cutter is nice to have too.
Over the years I've graduated from a 110 volt stick (Walmart), to a commerial 220v stick (Hobart), to a MIG (Lincoln), and now the Chinese TIG unit referenced above. Stick and MIG are quick, both in setting up and welding rate. The TIG takes me a little longer to setup and the welding rate is slower, but it provides more control. It is possible in some cases to use the TIG to weld the metal without filler rod, or to use miniminal filler. This minimizes later grinding if your goal is a smooth flush surface.