I will say that I'm a huge front projection fan, and this room really works well for front projection, especially with the ability to do a false wall pretty nicely with an AT screen.
I think my biggest concerns are that I don't know how the kids treat the room as a play area. This was a concern of mine, and I ended up using a motorized retractable projection screen and then built a lift for my projector to get it up into the ceiling with a smaller projector (BenQ W1070) which fit between the ceiling joists. Then I paired it with inexpensive speakers instead of nice speakers. Sound took a hit, but balls + bows & arrows fired in the basement hasn't hurt anything in the past 7 years, and now they've moved on to almost pure video gaming and I am getting close to really finishing the space.
It's a real question as you need to consider the kids and potential damage to equipment.
If the space is really coming away from being a heavy kids play area, or more of a play area behind the couch only, then a projector may work very well and you still could consider putting a lift together if you wanted to, but the fixed frame AT screen could stay in place.
At a solid 120" or so, with a 12'-13' eyes to screen distance you would get good use of the size and then could pair it with a solid Epson 5050 or JVC 790 projector (or nicer) as budget permits.
Even starting off, you can go cheap, then build up as you would like to.