Well technically speaking the ideal room has four unequal sides, so that the standing waves issue in most rooms won't happen. However I realize that may not be possible. Personally I kinda cheat and use a Receiver by Pioneer, it comes with a microphone and tunes itself, standing wave adj., phase control, and auto e.q. just to name a few. I know this sounds like sacrilege to a lot of Audiophiles, but given your budget this may be right up your alley. The Pioneer I use is a Model SC-61. I got it online for just under $800 dollars, with a warranty and shipping. It has several HDMI inputs, six I think. It excepts any Fiber Optic or Coax Audio Input and it also has the ability to Bi-Amp your Front Monitors.
As far as room design goes, I know when I built my office into one side of my garage, I kept it very simple.... you know K.I.S.S.or Keep It Simple, Stupid. Anyway I used 5/8" sheet rock with some reinforcement spread around the ceiling. I used insulation that is Alaska spec for the walls, which is 13 inches thick. I shoved that into the four inch wall gap. This was done to keep the walls in compression (like Hover dam), thus eliminating vibration.
The garage door was a different story, I started by inserting foam panels in the garage door recesses. Then I sealed up the guide tracks on either side using foam panels and expanding foam. The idea here is to get it close but with enough clearance to keep the door operational. Making the sound go around a few corners can have decent results for sound/temperature control.
As for the software question....... Myself? I don't use it much, have a medical condition known as Synesthesia, a crossing of sensory perception. Or in my case, I can see sound waves traveling around like ripples in the water. So I tend to stay away from software unless it saves me a bunch of math. I would recommend a book like the one I read before building my sound room.......called, Master Handbook of Acoustics fifth edition by, F. Alton Everest & Ken C.Pohlmann
Good luck, I hope I helped.