What is the best way from remove background signal from a band when doing Western blot image analysis?
I haven't done immunoblots for years, and didn't do much quantitative analysis of them even then, so caveat emptor. However:
1) &quot;Are there any ways to determine how wide you want the band for your background to be?&quot;
I would say that the central limit theorem is a good place to start. Basically, as the size of your background increases, the precision of your estimate of mean background intensity will also increase (asymptotically). So you want your background sample to be as big as possible.
This does have some assumptions:

Little regional fluctuation of mean background signal

(related) Absence of gel artifacts


So, you want your background sample to be as big as it can be without including any artifacts and as long as it is representative of the blot in the general region of your band. In practice, I imagine that taking a selection the size of your protein band is probably fine in most cases, and probably easier to explain. You just have to pick a representative piece of background to measure.
2) how can you know if you have made the rectangular band for the background too wide?
Wider than the blot is too wide. On an infinitely large blot, I think you can't make it too wide. For practical purposes, you want it to be as wide as you can get it and not overlap obvious artifacts or the edge of the blot. But again, it's probably easier to explain just selecting a piece of background as big as the protein band that is roughly near the protein band, to account for local background variation.