You could get a 220v class Mig (much higher amps and can handle thicker stuff) with your 220v outlet or you can run a real stick welder like the Lincoln tombstone you have in your link. You could get something like the Hobart Handler 190 but it'd be more money but you'll be able to handle thicker stuff. Welding supply stores often get local school machines or local shop machines on trade in too and go through them and sell them at a reasonable cost so you may want to ask at your local welding supply store and see what they have available.
It really sounds, however, that you are wanting to weld thinner stuff (light gauge angle, etc) and stick is a good bit harder to do well with that than other processes like mig and tig or even O/A (the smallest commonly available stick rod is 3/32, and while smaller stuff is available it tends to be commonly sold in tiny blister packs at high prices)
That welder is also an AC only buzzbox, not DC capable (AC has to use different rods than DC, like AC can't run 6010 or 7018, it has to have 6011 or 7018AC, which has stabilizers in the flux to deal with the AC's arc characteristics). Probably fine for your case (i.e., 6011, 7018AC are the rods sold at Home Depot/Lowes/Tractor Supply so the supply isn't an issue) and plenty of stuff has been built with AC tombstones just like that one.
You can also get one much cheaper on craigslist, like for around a hundred bucks in good shape.