If your wife your master? Or wife and master are different people :|
At first, when I read it, I thought that "budget for Santa" meant that they give you some money to dress as Santa; but now I understand!
(I think!)
I've read that the 50-500 is big, slow and noisy, but that is only what I've read a while ago, nothing that I've actually experience for myself.
Ask Santa what you should get.
I'd prefer the Canon 100-400L to the Sigma 50-500 though I've not seen either.
I think zoom lenses are quite convienient - getting all those focal lengths in one; as compared to shooting primes where you would have to move around (but another thing that I read (YES, this is all based on what I read! not what I experience myself! so... sorry if I just sound like I'm repeating other people's comments) is that prime lenses have less elements, and ummm *something*, so they are supposed to be better in image quality that zoom lenses (the relevance of mentioning this is in response to the "Or would I be better off getting a range of shorter lenses") I think one with a large zoom range would be good as you don't need to keep changing lenses when you decide to shoot something else. But the trade off is that (again, from what I've read, not my own opinion) the lenses with larger zoom range tend to be softer.
I guess it also depends on what you'll be taking photographs of.
Sorry a lot for just repeating things I read. Hope you don't mind