Okay, I found a nice, seemingly easy to use mod for PHPBB3 that I'll be putting up tonight/tomorrow. It hosts pictures here on the website host. I'll drop our hosting company an email and let them know about the upcoming mod, so they'll know what's going on if there's a jump in traffic/bandwidth.
I'm not opposed to paying a little more out of pocket for hosting if we need it, but if things get insane I might have to look into other options, or put up a donate button if anyone wants to chip in for the hosting costs.
Also, found another mod that auto-resizes pictures to a pre-set max, with the ability to click on them to open them in a new window/tab in full size. Once I make sure the first mod is working, I'll install the second and see if they play nice.