The only real limit to how thick you can weld with a 110 welder is your Patience. The welder's duty cycle and the fact it is restricted to small wire will of course make really heavy welds quite impractical even if possible but there is no reason for the weld to be inferior if heavy sections are preheated first and the weld is made in multiple passes. Preheating the base metal to around 400 deg (just too hot to touch with your bare hand) is the key to making strong welds with small wire and heavy sections, attempting to weld onto cold base metal over about 1/8" thick results in brittle welds due to thermal shock and under-bead cracking.
I personally am no big fan of flux core wire but Lincoln MP211 seems to be a really good wire that is widely available, any welding supply, Lowes, TSC, Northern Tool and believe it or not even Wal-Mart has it here. No offense meant to the suggestion of HF wire but I would strongly advise avoiding any welding wire from China!
The weld you make is only as good as the filler you use and the make-up of welding wire, especially flux core, is critical to a weld's success and Chinese wire is of highly suspect quality! Alloy content, trash in the flux and poor sizing tolerances make the stuff risky to use and since good high quality name brand wires are so easy to find it makes no sense to chance making a weld with what is in all likelihood scrap wire. I buy several things from HF but I would not carry that welding wire out of there if they gave it to me! Welds are not something to scrimp on and failures can range from just being an annoyance to being very costly or even deadly so always use a filler wire of known and verifiable quality, any of the well known brands will meet that requirement.