I'm not exactly sure -- MSVC in Windows will happily chug away on 3GB with the incremental linker, but I don't know if it needs to be doing that, or what it was doing in Linux. I should have taken some notes. Not sure if experienced Linux people can tell me offhand if 1GB would be fine for a reasonable bulky project.
The DFHack build server for Linux and Mac (yes, they're the same machine) has 3GB of RAM split between all the stuff I run on there, and right now there's a DFHack build running and htop looks like this:

That's the highest the RAM usage has been this whole time I've been watching it - usually it's between 300MB and 700MB for the whole system. 1GB should be fine, and as long as you have
some swap space, your build process won't crash if you use more than the gigabyte of physical RAM.
If you're running Windows 10, you can enable a Linux kernel emulator by going to
Control Panel\All Control Panel Items\Programs and Features, selecting
Turn Windows features on or off, and checking the box for
Windows Subsystem for Linux (Beta). That has the advantage of sharing a memory manager with Windows, so unlike a virtual machine it won't use up memory and not release it until the virtual machine shuts down.