Most digital cameras work under Linux, if
- you are prepared to use a file manager to move files around (rather than wanting some integrated app)
- you are happy to use jpegs, rather than raw files
if you want to use raw files, be aware that raw isn't a format, but a collection of vaguely related file formats and you might have to get a proprietary program to deal with these (...or not, depending...). In that sense, point 'n shoot compacts are probably easier than DSLRs as you probably want to use the RAWs from a DSLR.
In the early days, there were some compacts that would not mount as a storage device, but I think that's over by now (sometimes you have to delve deep into the menus to set them into the right mode, though).