I recently installed a mini-split to heat and cool a 550 square foot rental. I pay the utilities on this rental, so I wanted it to be more efficient than the window units that had been up there for years. The garage apartment is 100 years old, with single pane windows, no wall insulation, etc, and man can this thing heat and cool. It uses heat pump technology, and it can put out some serious heat. I paid about $1200 and did all the install by myself. It looks like the price has gone up to about $1400 which is still a pretty good price considering. Its in Houston, so similar heating and cooling needs to NOLA. I was surprised when I was showing it this time around at how many people commented "oh, finally, an apartment with real A/C. What I used was a Mr Cool DIY 18000 BTU unit, which required 220 service, but your space sounds smaller, so you might get by with the 12000 BTU that uses a (dedicated) 110 circuit.