You want to know the screen resolutions the laptop can generate on the external video connector, to match to what the projector can accept or scale to. We had a very old projector that would only accept 640x480 from the computer, none of the current laptops could go that low of resolution, so the projector was not usable on any modern hardware. The projectors have gotten smarter and can accept a broader range now and can even scale down resolutions, so this should not be as big of an issue as 10 years ago, but could still show up if you get a donated projector. And as usual remember the cost of a replacement lamp which can be from $125.00 to $500.00 so a donated projector with 2000 hours on the lamp will cost you a replacement lamp to get started.
If you purchase a projector, really try to work with a local vendor who may have a spare machine if yours breaks, can help with training and troubleshooting, and can be accommodating if you need to borrow a projector when you over book your projector. Some of those services can be worth more than the couple of dollars you save buying on line.
Dave