We don't know what the OP is attempting to compile. It might be just some code to run inside the Arduino bootloader, or it might be a whole muLinux and a local GCC for the target. Heck, the Debian distro for the BBB might not have a binary for the target muC, which means compiling GCC before compiling the code (worst case). There is also the possibility of OPs chips not being supported in GCC. For example, I just picked up some Cypress PSoC boards; the tools for them are only available right now on Windows. Not ideal, but writing some C so GCC could mangle the analog portions of the PSoC would be more uncomfortable imho.
Unknown target devices, unknown tools, leaves me suggesting something a little more capable than a embedded device. While a windows x86 device might not be ideal for all folks, it might be necessary for some target device's toolchain. I have a several year old quad-core i7 with a geforce 560 and spinning drives that runs on less than 100 watts; one could use an older second hand laptop like that, or a newer even lower power one with an SSD. It's not what the OP asked about, but the OP also didn't provide enough information to presume that they knew what their target embedded muC might always be. And for the general case of other readers who are reading this, I think a small laptop is still the best choice.
Sorry for all the mu, I can't seem to get the html for μ to work