what connector for output does your laptop have.
VGA D15, small D shape with three rows pins - https://en.wikipedia.org/wiki/VGA_connector
DVI-?, slightly larger and with several options - https://en.wikipedia.org/wiki/Digital_Visual_Interface
HDMI like your telly and now most common for some time. https://en.wikipedia.org/wiki/HDMI
If you can share what model of laptop/device you are showing from I can help more.
By priority of benefit IMHO.
Lumens - how bright and so how dark the room needs to be - bigger is better. Older units have a more limited life on the bulb as it burns out but this will be ages for most home users. Modern units use DLP which is better.
Resolution - In general PPT likes a 1920x1080 resolution these days but usually can work on lower if needed so the ideal projector will provide this (FullHD)
There is a bit of a cheat floating around here. They will claim FullHD but when you look in the technical spec it actually runs at a lower res and the electronics fake this out to the laptop to make it think it is actually FullHD.
This is not a massive problem but means the screen might not be so perfect. For £500 you should expect real FullHD.
As an example you will see on this site (eBuyer) the resolution and "native" resolution options down the side https://www.ebuyer.com/store/Visual/cat/Projectors?q=projector&price=20+TO+588
If it is any help I have an older one I used to use in my office which has been retired from daily use. More than happy to do you a small price and shipment, where are you based ? I can get the spec if you like?