I have absolutely ZERO Mac Emulator experience, what OS do they run under?Are they each an OS in their own right?
They're not "OSes in their own right", they're just applications. To use them you need a ROM image and a disk image (which is just a data file that acts as the hard disk for the running machine). You install the application, point it at the ROM and disk image, and you're off.
Both SheepShaver (PowerPC, runs up to 9.0.4) and BasiliskII (68k, runs up to 8.1) work fine under Linux, and I'd actually argue they're better under Linux than they are under either OS X *or* Windows. (Simply because Linux/X11 is the native development platform, the other versions are ports.) But any will work. Your Mac emulation can run inside a window or if you're so inclined you can let it occupy the full screen, and both BasikiskII and Sheepshaver have a feature that allows you to map a virtual drive inside the emulated machine to a directory on the host filesystem, allowing you to drag and drop files between the two systems.
Googling something like "Sheepshaver Ubuntu" will net you plenty of resources for setting up the emulators if the links already thrown out are not enough. Really the only requirement is that you need a ROM image from a supported Mac (although in the case of SheepShaver and OSes newer than 8.5 you can usually use the New World ROM image that comes on the installation disk) and installation media or images for a supported OS. (Which can make Sheepshaver a little bit of a pain because it has a hard limit of 9.0.4. 9.1 or newer disks *will not and will probably never will work*.)
As for performance, both Basilisk and Sheepshaver are faster than any "real" 68k Mac on even fairly slow CPUs. (I've been using BasiliskII almost since its introduction around 1999, and even right after the introduction of their first JIT CPU emulation core a 166Mhz Cyrix machine could benchmark about 80% as fast as a Quadra 605. With the older interpretive core a Pentium was closer to an LC, which obviously was a huge difference.) I haven't benchmarked an Atom but my vague guess based on how fast SheepShaver is on the slower machines I have used it on is that an Atom should easily be somewhere in the 603e-early G3 ballpark. (Faster on some things, slower on others, your mileage may vary, etc, etc.)