My advice would be to first determine your room layout so you can figure out what size screen you need and how you want to arrange seating and the rooms other features.
Since this is going to be a multipurpose room I would suggest that you buy a screen with a gray screen color to help combat any ambient room light. Depending on how much you want to spend there are products from companies like SI that offers a product it calls “Black Diamond” and it’s designed for multipurpose room environments. Other companies that make more affordable products include Elite Screens.
There are plenty of HD projectors from companies like Panasonic, Mitsubishi, Optoma and Sony that cost about $1,000. There are also lots of flat-panel TVs on the market worth considering from top manufacturers like Samsung, Sony, Panasonic and LG, to more value-minded products from companies like VIZIO.
As for audio, you can find a good A/V receiver for $500 to $800 that will do everything you ask for, including iPad/iPod Touch/iPhone control capabilities. You’ll also need to determine if you want in-wall speakers or in-room, freestanding speakers.
Another consideration is to think about Internet connectivity for this space. If the walls are open you can run network Cat-5 Ethernet cabling, and there’s other options such as wireless or even a technology known as powerline.
There are also lots of remote options from companies like URC that vary in price.