...I will look for a used AC/DC ( I know what that means for electricity, but not for welders!) stick unit as advised above by rankrank1...
Well in general DC will allow you to run a broader selection of specialty rods and is slighty easier to use in striking the initial arc, maintaining the arc, and welding in out of position areas. If you have DC you will rarely use AC. That said if all you plan to weld is mild steel then AC is fine, cheaper, and even a tad bit more reliable in a buzzbox, but I would opt for the DC capilbility as it gives you more options to grow and speeds the learning curve for a newbie.
Really all a welder is a glorified adjustable voltage converter. The Welding process is designed to be a low volt and high amp process. If welding worked well with high voltage and low amps then we simply could use the AC power from the household circuit panel to weld, but that will not work well.
Take any of the buzzboxes mentioned in my original post (lets have the welder set at wide open setting to keep this simple):
a) Household input power is roughly 230 volt and roughly 40 amp. If welding was a high volt and low amp process then we could simply use the household power but its not as already mentioned which is why the welder is needed
b) At wide open setting on welder AC you have 79 volts Open Circuit voltage and 225 amps of power. OCV voltage of 79 will drop to 30-35 volts when actual welding is occuring. Welding works best right around that 30 volt area - the higher OCV simply makes it easier to strike the initial arc.
c) If the welder has DC capability then a rectifier diode bridge will be used to convert the AC to DC power. More loss will occur in this conversion to DC which is why most DC buzzboxes will be in the 150 amp range.
So what does it all mean:
On AC your arc is actually going out at a frequency of 60 hertz. Just like you lights in your house are actually going out at 60 hertz although nearly impossible see with human eye. There is no such thing as Polarity on AC as the Polarity is switching from positive to negtive at a frequency of 60 hertz. (With no Polarity then kinda think of it as 50% heat into rod and 50% heat into workpiece).
On DC the arc never goes out making it a little easier to maintain an arc and there is such a thing as Polarity with DC. With the Electrode Positive and work negative you will have roughly 67% heat put into the weld rod and 33% heat into workpiece which results in max pentration and is the most common way to run. With DC electrode negative and workpiece positive you have roughly 33% heat put into weld rod and 67% put into workpiece which results in less pentration and can be useful for specialty applications and when welding those metals that are near the thin 16 gauge thickness. Less penetration makes it easier to avoid burn through on thin metals. Many specialty rods like hardfacing rods will only burn on DC. But if all you do is weld mild steel then there are rods that burn fine on AC but these same rods will usually burn 15% better on DC. In short if you have DC you will rarely use AC.
As already pointed out a buzzbox gives you much more than a simple welder. You can also use it to crudely cut metal as well as to heat metal and braze metal with with nearly zero consumables. It gives you a lot for a mere $125 investment (used AC unit) or $250 investment (used AC/DC unit). Only thing it will not do well is weld metal thinner than about 16 gauge (roughly 1/16" thick).