I'm not a welder by trade, but I've done a fair bit of welding.
I personally have a millermatic 210 which can weld 3/8" thick steel in a single pass.
Since you are limited to 110v and have never welded, a mig
unit is your best choice. Get one that is capable of using
either flux core or shielded gas wire. They each have their own advantages.
A 110v mig unit is very versatile unit, being able to weld thin gauge sheet metal up to about 1/4"
with a single pass, depending on the welder. Granted they don't have much of a duty cycle.
Do buy a brand name unit such as Lincoln or Miller. Century is also a good choice.
Also as mentioned, get a auto-dimming helmet, it makes welding a lot easier.
Here's a couple of places to visit.
Joint preperation is the most important thing for a good weld.
Clean the surfaces of oil, paint, rust etc. before welding. When you do start to weld,
don't get discouraged by what your welds look like, just keep practicing.