TIs this what you guys consider a "buzz box" because it sure does buzz when it is running. If you were to recommend a stick welder other than that one, what would you recommend?
A "buzz-box" is a transformer-based stick welder, and that's exactly what you've got. People usually, in my experience, use "buzz-box" to refer to low-end AC-only machines, but you can get more or less the exact same machine with both AC and DC output. It'll buzz the same either way.
I don't have enough broad experience to recommend any particular welder, but I will say that you almost certainly should consider getting a DC-output welder if you are looking to trade up. DC is nicer to weld with for stick, and it opens up the option of moving to scratch-start TIG in the future, which is a great way of expanding your options without too much extra cost.
Another consideration is whether you want a transformer-based machine or whether you want an inverter-based machine. The main advantage of transformer-based machines is that they are simple, have few parts to break, are easy and cheap to repair if they do break, and they don't cost as much up front. The advantage of inverter-based machines is that they are lighter, they are more efficient (produce more output for less input), and they have all sorts of awesome bells and whistles like arc force and hot start. Inverter-based machines are also often said to produce a much nicer arc and offer much better puddle control, even in the lower price range; transformer-based machines can be just as good, but you generally have to pay more to get there. Again, I don't have enough direct experience to say that personally, but that's what I've heard. On the other hand, inverter-based machines are more expensive up front, and they have a bunch of computer circuitry in them, so if they break, you basically have to order a new board or component from the manufacturer. There's not much on them that you can repair yourself. Additionally, it remains to be seen whether inverter welders will have the staying power of transformer-based welders. There are fifty-plus-year-old Lincoln buzz-boxes that are still working today. If I blow a diode on my welder, I will be able to buy a new one from any electronics supply store. With an inverter-based machine, if, fifteen years from now, the manufacturer has discontinued the line, will they still be producing the circuit board that you just burned out? Maybe, but maybe not.