Best image dimensions for downloadable wallpaper, for PC, HD, mobile and tablet?

You probably need to think first on the proportion.

The classical proportion

The classical (oldie) porportion for desktops is 4:3 for example.

• 1024x768
• 1280x960
• 1600x1200

Some pads use this same proportion for example the ipad uses:

• 2048x1536

Vertical orientatnion

This takes us that this pads used in vertical orientation gives us a 3:4 proportion which would be inverting the values.

• 768x1024 for example

The widescreen

The main proportion is 16:9

• 1920x1080
• 1366x768
• 1280x720

You have the same case if you want a vertical orientation 9:16

Variations

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