How big should I allow images?

On my site, it has come the time to allow user uploads (just images). There are two sizes of images that I will allow:
A profile picture (so the smaller of the two)
And a "team" profile picture (this one is the larger of the two).

My question is in general, what should the width/height maximums be set and what should be the max size (in bytes) for both of the images? I have looked around on different sites to get a feel, and there does not seem to be a consistent one size, but 3Mb pops up a lot.

3mb is a pretty large image. That is about the size you would use if you were allowing full screen shots in a bmp format (which you shouldn't allow because they are ugly and oversized usually) on like a forum. As for the size of images for profiles and such, you really should just figure what size fits into your webpage layout the best and make it that size in width/height. You shouldn't really need anything larger than like 200x200 for a profile image. And I feel that 50k is more than large enough for a jpeg image of 200x200. Do a google image search for anything to get an idea and it should show you height/width and size. You can get a pretty good idea of how large an image should be.