I don't weld anything thicker than 1/2" for my wrought iron work, so your thick plates are a bit past my experience personally. (At work ... well that's a different story. But at work, the professional welders are doing their thing, and I'm only QA and safety and paperwork and job orders and work permits and fire permits ...))
For my uses, a 240 volt Miller or Hobart MIG with CO2-Ar mixed gas is perfect: Very good penetration at the higher power settings, dialed down to a "1" setting I can join thin gage sheet metal or gratings. Almost nothing to clean up (no BB's and no slag) and you can weld indoors (garage or basement) with little issues other than a fan or filter. My steel is usually "new" - I prime and paint afterwords, so there is no rust issues with any type rod.
Outdoors? With a cardboard or wood shield, I've not had problems with the MIG.
I do have a Miller "little blue box" that is TIG and stick (SMAW) capable, and have used both successfully. MIG is faster than either, and I feel I have the best control and best looking welds with the MIG.
Stick cannot be beat when I'm up a ladder or on scaffolding though: Just a single cable to pull up (instead of the whole machine plus the gas bottle and gas line extension) and you use stick one-handed if access is poor or you're working overhead. Durty, smoky, flame-producing, lacks of spatter and lots of slag to chip off. Start & stop opertioon as you change weld rods slows stick down.
if you have a real small SMAW machine, you still can't get good penetration; so get to a weld shop - NOT a Sears, Home Depot, Lowes, or Ace Hardware. NOT a "Orchard Supply Hardware", or cheap import place.