Background Textures and Resolution

When choosing a static background texture, which resolution/size should I be looking for? If it is too small, I assume it will get stretched (or repeated)? Do I just go with a high version so it covers more users?

I suggest using 2048x2048. Disable mip maps to save some memory too, since you know you won't need them. You may also want to create a 1024x1024 version to use instead if the current resolution is 1024 or less wide.