Let's say I wanna make a website that would allow a user to download a wallpaper in sizes for PC, HD, mobile and tablet.
What are the top used / best image dimensions I should host?
You probably need to think first on the proportion.
The classical proportion
The classical (oldie) porportion for desktops is 4:3 for example.
Some pads use this same proportion for example the ipad uses:
This takes us that this pads used in vertical orientation gives us a 3:4 proportion which would be inverting the values.
The main proportion is 16:9
You have the same case if you want a vertical orientation 9:16
There are a lot of variations in proportions and resolutions. You can take a look of them on this image from the wikipedia (the circles show the proportion):
So the truth is you need to take descitions on the target you are aiming.
You can look some trends using this google search https://www.google.com.mx/search?q=screen+resolution+statistics
Common sizes for desktop are 800x600, 1024x768, 1280x1024 and 1600x1200
HD usually means 1080p nowadays so that is 1920 x 1080.
And this Google Browser size diagram may help