The Lincoln you listed looks OK, but is pretty weak on power output, I think the specs are 88 Amps, 20% duty cycle at 70-Amps, and a fixed flow regulator?
I just looked up the Eastwood 135. Specs look better, 125 Amp max with 20% duty cycle at 90 Amps, had an adjustable regulator, and is on sale for $259.99 (price seems too good?)
Get some solid core wire and a bottle of 75/25 CO2/Ar will give you nice clean welds. Flux core wire is ok, and should be used in areas where wind can blow the gas shield away, but it spatters quite a bit, and burns a bit hotter than the gas shield which is important when working with thin sheet metal.
If you plan to weld often, you will likely outgrow these smaller welders, but the next cost point is at least double the cost of these entry level welders.