How to choose a small projector and a small computer to it?

Question

Projectors

Advise a small projector and a small computer to it, possibly on an android.
Purpose: I want to make an informing "tableau". Information from him is needed only at night, the image will be projected onto a wall with light wallpaper. Strong brightness is not needed, so as not to interfere with sleep, you only need a slightly noticeable image, like in a projection clock, which does not illuminate the room. The idea is this - it constantly displays some nonsense, for example, the temperature in the room and on the street, or the weather forecast, the exchange rate of some currencies, bitcoin, for example, time, etc. And when the alarm is triggered in the car, then the image from the IP camera monitoring this car should be displayed.
I see it like this: there is a Synology server, a page has been created on it, so far only with the bitcoin rate, temperature from arduino, and a second page with an image from the camera. A small computer connected to a small projector. The computer displays a web page on the projector. When the alarm key fob is triggered (it has vibration), either the computer should go to another page and display the video from the camera, or the page content should change on the server, until I know how to do it right.
You can also disassemble the projector and adjust the brightness, it is not critical if there is no standard adjustment. When the signaling is triggered, make it a little brighter, if you can pull out the brightness during the day, then you can turn it on all the way so that it can be seen during the day.
A projector resolution of 640x480 will be sufficient. Color rendition does not matter, 16 colors is enough, or even bw. The distance from its position to the wall is about 3 meters, while the image needs to be about a meter and a half diagonally. preferably the most compact version, without a cooler and other noises.
Computer - as small as possible, also absolutely quiet. Maybe a flash drive on android will do? Communication with the web server - WiFi, Ethernet cable. Or maybe there is a projector with a built-in browser?
Everything will work 24/7.
Tell me who about what. I have never held any projectors or small computers in my hands. Google is of course to help, but there are all sorts of pitfalls.
The budget for everything is ~ $ 500, something is possible because of the hillock.

Answer 1

Straight news for you: www.iphones.ru/iNotes/343874
In general, google pico projectors, there are a lot of them. Comp - flash drive or nettop.

Answer 2

I recommend the ViewSonic LightStream PJD6352 projector. I have one, I bought it here ict16.ru/catalog/multimediynye-proektory