Ok, I'll bite...I'm looking for the opposite of an enthusiast setup with this one.
A family member wants to bring a projector and screen outside on Friday nights to display movies and cartoons for their and their neighbor's kids. We're talking a group of 1-4 year olds. They'd like a portable/inflatable screen, a projector, and probably a single powered speaker. It will be dusk or dark outside and they'd like about a 120-150" screen. Distance doesn't matter as they'll be running it off an extension cord and probably a stack of crates.
They already have a "real" projector setup in their home theater, so this doesn't need to be something that can grow with them. The cheapest solution that doesn't literally burst into flames is the goal. Refurbished is fine, but also open to no-names. Since it'll only be a few days a year, bulb longevity also isn't critical.
Any thoughts? Can they get away with this for under $600?
"We're talking a group of 1-4 year olds." ...
Well, assuming you're located in North America, it doesn't really get dark enough to use a projector until around 9:30-10:00PM. I don't think you're going to have much of an audience that's still awake at that time if it's a group of 1-4 year old children.
With a group of 1-4 year children and a $600 budget, your best bet is to go over to Costco and pick up a 65" $600 LCD TV or the biggest LCD TV you can find for $600.
You'll be able to watch it outdoors with some sunlight or start at dusk with picture quality that will attract 1-4 year old kids. The kids won't know that it's not a 150" screen and nor will they care. You won't have the disappointment and problems that a cheap inflatable screen brings to the party. The TV will work very well with an extension cord. There's little to no chance that the TV would burst into flames, and you probably won't need a stack of crates or a powered speaker.