Part of me has been tempted to try out one of those cheap projectors on Amazon just to see how good they are. You know... the ones from Alibaba that get rebadged by about five different companies, but they still look the same (apart from the logo).
They're probably kind of junky, but for $75, it's not the worst thing.
I've worked with a ton of projectors and it's a toss-up. The super-cheap projectors are not great, but it depends what your standards are. I have a buddy who never had a projector & is totally in love with his $99 Chinese VGA projector. I gave a $75 UC46 (800x480) to my nephew for his birthday & he plays old SNES games on it & it's pretty cool. But my friend got a competing model with the same resolution & it's really awful...focus doesn't work right, among other things. So it's kind of hit & miss. I would also say, it's important not to judge projectors by the cheap ones...a lot of people buy cheap ones & get turned off to the idea. The XGIMI H1 is liking having a Samsung LED TV jumbo-sized on you wall, it's
really amazing. Cheapo projectors are fun just because you get a big picture for cheap & it's really cool to get a taste of the big screen.
I would say, for you, since you watch a lot of anime cartoons, go for it - cartoons are
way more forgiving on the cheaper projectors than live-action movies are because you know what a real-life person is supposed to look like in a live-action film, and cartoons are colored images that can still look fantastic at lower resolutions. The most important part of using an ultra-budget projector, because the lumens & contrast numbers are low, is remembering that it will do best in a pitch-black room at a smaller size (like 50 or 60", which is still plenty big). If you are serious about getting an el-cheapo PJ & have a few extra bucks, I'd recommend springing a little bit extra for the AAXA HD Pico (~$135 shipped) because you get a real HD native resolution (720p), plus it's tiny, which is wicked cool, and it's LED, so no bulb to worry about. I can make a quick video with some anime clips if you want to see what it looks like (also has a built-in battery, which is cool...you can plug in an HDMI adapter cable from your phone & use it in random places, like a bedroom ceiling or camping or whatever). In terms of PQ with anime stuff, AAXA used to sell a short-throw projector (you can use it close to the wall, which is convenient to just put it on your coffee table) called the ST200 that was only 150 lumens, but still looked great: (they have it available refurbished for $209 directly from their website FYI)
If you have a bit more of a budget and want a REALLY decent 720p LED projector (which can do up to a 120" screen pretty dang well!), the P300 is quite amazing: (good enough to use as your "TV", if you have a dark room like a basement or some blackout blinds)
https://www.amazon.com/AAXA-P300-Neo-Video-Projector/dp/B074QK249C/
So the LED projector quality scale is something like:
1. $50 to $200 = hey cool, a big picture on your wall - super neat introduction to the incredible world of projectors
2. $250 to $600 = wow that's pretty great, very impressive (again, the P300 is a gem in this price range)
3. $850+ = that's a real, amazing home theater projector