Maybe a PDP-11/03 or 11/23? Too noisy, I think. And while RT-11 is lovely, I'd be limited to writing text, C, and Fortran. Oh, and PDP-11 assembler (maybe just punch the opcodes in in octal, as it's so easy to translate in your head on a PDP-11).
Amiga 500? Nope, won't run GCC.
A 286 or a 386 is looking more serious. Some of them have a good 8Mb of RAM, VGA output and ethernet. Could even run linux, something like 2.2 from the days when a system worked well with 4Mb RAM.
Any 486 would definitely do it, all the 486/66 boxes just turn on and go (one has been doing daily duty as an autoattendant for maybe 15, 20 years). Starting to get to the point where there's a DVI output, so nice text on an LCD (the massive 27" Diamondvision CRT can stay wrapped up).
Hmmm....now, a Gateway 166MHz Pentium. That's nice, because it's pretty much silent, runs 100Mb ethernet and has a Matrox video card. Zero problems working with that for a week (or longer) except for web browsing (there's always links/lynx et al).
An 800Hz PIII with 512mb of RAM and an Nvidia 7600GT video card would be fantastic - those video cards were the fastest text kids on the block (scroll about 600k characters per second at 160x60 on 1600x1200 framebuffer). XFree86 from 2004 works fine, but a web browser would have to run on a faster box and export the display (which would be cheating). Old versions of Firefox are plenty fast enough, but will crash PDQ on many modern sites.
So really it'd be the modern web holding me back; too slow, bloated, and inefficient to run snappily on pretty much anything short of a 4GHz+ multicore with 8Gb or more of RAM and at least 100Mb ADSL.
Think I'll go cry into a paper tape reader now....