MS-DOS was 16-bit, and was pretty happy with 1 MB of RAM, but it had no graphics, no sound, no threads, and no internet support.
PC DOS 1.0 (the IBM-branded version of MS-DOS) took up about 12kByte of memory.
The ZX-81 (contemporary to IBM-PC's and MS-/PC-DOS) ran a text interface and BASIC interpreter off a 8kByte ROM chip and 1kByte of RAM.
Windows 3.x had all of this, and required up to 3 MB of RAM, depending on version and CPU.
You may find some OS out there that has better functionality and lower system requirements, but probably not by much.
AmigaOS 1.x ran off 256kByte of RAM and a 256kByte ROM. 32bit, GUI, 8bit color, 4x8bit stereo sound, preemptive multitasking. (That's about contemporary to Windows 1.0 by the way.)