Air conditioner and air purifier?

We recently just moved in to a 2 bedroom appartment and it seems like theres always alot of dust in the rooms. I always open up the window because if i close it, the room would become really hot. Its like summer months now, but still i always clean and wipe my furnitures but somehow alot of dust settles on it. I bought an air purifier yesterday ( honeywell,with the true permanent hepa filter) i can truly feel the difference of the air quality in my room. but iwas wondering if i buy an air conditioner/portable ac for my room, would it be better to get absolutely no dust in my room….because it says that the air purifier would work best if all windows are closed….and if i buy an ac i can do that….please give me any suggestions…thanks. and is there any difference between the window ac’s and portable ac’s.
im planning to buy a portable ac because i dont think i can fix the window ac by myself…and i heard portable ac’s are easier to fix……please let me know…thanks !