My experience with OP1 in XP:
If you get the 16-bit insufficient memory error, restart in safe mode and play the game. Very few processes will be running, which allows the application to work properly. It also makes sure that no other 16-bit apps are running, which can sometimes interfere with it.
I went back to my old patched version from the original CD. There IS a difference between version 1.5 and 1.51. Version 1.51 appears to not be stable in XP, and encounters frequent "stack overflow" errors, or other errors for unknown reasons (like dozing certain buildings, or building sometimes, or even just going to the next turn after awhile). Version 1.5 doesn't seem to have this problem, but a couple of the dialogs appear blank (it is trivial to the gameplay). It also doesn't leave the screen black and green most of the time. I can upload this version if someone wants it; the only download from this site is version 1.51.
Something that might help in both version is to not run the program in Win95 compatibility mode or with any other compatibility options enabled. This appears to cause errors as well.
Also, don't keep the command center window open like I normally do. Having any building windows opened seems to cause a crash when they go to update on a new turn.
UPDATE: Doesn't matter which version you use, there are still problems on most machines. The solution I found was to get Virtual PC 2004 from Microsoft (it's free), and run it inside that emulated environment. It runs perfectly. It took hours to find and properly install all the stuff for Windows 3.11, but I can simply post the Virtual Hard Drive image from my emulator and save you the trouble!