If you had something like this
You can put virtually any kind of light setup in it especially with a good fan. HPS, MH, LED, Induction, CFL. [Led's, Induction and CFL;s {T-5's etc} will generally run cooler than HPS MH]
400w HPS or MH is probably your max although a 600w would saturate it and I don't know if anybody would recommend anything above....
A 250w HPS would give you what you need once dialed in.
LED's are the route I would go if I had loot. One quality light from an
American manufacturer would be plenty for a 2x2.
Reduced maintenance over the long term and upgrades easily possible. Same for induction although they still tend to run a little higher.
CFL'= tubes are also an option and might be the cheapest in the short term, but maintenance cost like HPS/MH, are largest overall in the long run, [replacement, maintenance, heating and cooling] as compared to the other types.