Thanks! Emscripten is the tool that makes it relatively easy, for stuff with source code available. So I'd say pick something and try to build it with Emscripten.

For stuff without source code you'll have to use emulation. DOSBox and MAME have web ports already. I haven't looked into them much. But the Internet Archive has a big collection of games that run in them already. So check that to see if the game you want is already available.