I have some bad news and some good news
First the bad news: You may find the budget some what tight to do a good job and the basement usualy meens a low cieling height.
Now for the good news: The location of your house and being in the basement will go a long way to reduces the need for extreme sound isolation measures. The walls of the basement are probably concrete or cinder block with earth on the outside. This should serve to control sound leaking out of or into the house relative to your neibourhs. You should be able to get away with filling the spaces between the floor joist with fiber glass bats, adding some 2X4 blocks between them and doing a tight sheet rock cieling to seal the top. That would leave you with only one or two walls that need to have a low transmition figure and anything else you do will just to control reverb.
The Ideal room would have a mildly trapasoidal cross section in all three planes with the back wall having a very gentle convex curve to it. The smaller of the two parallel sides of each trapasoid would be the front wall. This would leave you with no parrallel serffices. It is also desireable to not have any two major dimentions share a mathamatical factor. (The next time I go to the library I will dig up the peffered ratios for you) All this serves to smooth out the reverbarant field and diminish the effect of standing waves in the room. Doing it with the shape and size of the room makes the fine tuning a lot eazier and less costly. It would also serve to focus vision twards the front and the screen
If you are tying into the house HAVC system you need to decouple the ducting for the room from the rest of the house. The ducts need to be lined with fiber galss to absorb sound and should make at least two right angle bends between the room and the rest of the house. They should also be resiliently mounted to decouple them from the structure. On the house end of the ducts you want to use a short fabric duct to ferther decouple. Double the cross section and slow the airflow to reduce niose production at the regiters.
Try to think of a way to have the equipment rack in a pass through the wall with a heavy, stiff door on the front to remove any noise from the room. Use as much remote control as you can. Try to use lighting that is very efficient and also quiet -- less noise and heat to contend with. You are not trying to do quality control so you don't have to be to strick with color temparature in your lighting but you do want some light around the screen and I would go for some controled lighting for any tables and walk ways.
I am going to stick my neck out a recomend againts using even the best computer speaker systems even though they do come with an included amplifier. These systems are designed for what is called "near field" use, from one to three feet away from your ears not eight to ten feet to the front row in a home screening room. I saw some decent sets from Warfdale, Infinity and JBL at CompUSA today. I sugest that you make those a starting piont in your chioce of speakers. You don't need to buy those particular ones but get a good matched set, all of the same manufacturer and all using the same drivers for high and mid range. This will go a long way to nail down the localization of sounds in the sound field. If you don't go for exotic speaker cables get some really heavey wire 14 gage at the smallest and #12 for the subwoffer. It's not the current that the amp is sending to the speaker but the back EMF from the voice coil that matters. In this day and age do as much as you can in the digital domain, use optical cables to connect the system. A to D convertions are murder on Audio.
If you can raise the floor for the second row and all the way back to the back wall about 6", it will improve both sight llines and the sound for those in the back rows.
I hope this helps.
Grayson
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