best low cost movie projector option

Hi folks - so a couple of weeks ago my teenage son had a birthday party at the house, and on the fly I picked up one of those $50 projectors, to project on the side of our house, so he and his friends could watch a movie. I got it, tried it, picture was just fine for what we needed, so long as it was pitch black. Sound was terrible, so quickly picked up a bluetooth speaker, and it all worked great, he and his friends had a great time with it.

So much so, I thought we should repeat, and maybe even do a family movie night etc. - but, on just the 3rd time, the projectors sound output broke! So, I got online and started taking a look at a replacement, and quickly found my head spinning at all the information, ratings, lumens, brightness, DLP, all that stuff. After dozens of 'the hook up' youtube videos (amazing content!), Reddit threads, and hundreds of Amazon reviews, I've found myself paralyzed to move forward. I don't know what to get.

Budget is the chief concern...really sub $200 - this is just going to be a once ever 1-2 month thing, and on the projected wall of the house at nighttime, so the quality doesn't need to be amazing. I have room for a 12-13' picture, I have an amazon firestick, and a bluetooth speaker. I'm just hoping to have something that gets a decent job done, and won't break in a couple of months. I don't mind buying used either, and I can wait for a sale or wait to find something used that comes available.

Would love some suggestions - thanks in advance!