Why is it that whenever I play the beta release version, if I don't go back and tell Launcher where Legacy is, where doom.wad (I'm currently running of the original Chex.wad) and where Phase II Beta 3 is, I get a weird hybrid of Doom and Chex Quest? (flemoids give of blood, Single Player And Multiplayer appear in their Doom style, etc.) Shouldn't I be able to click launch without having to reset everything?

Well you did most of it right. However if you want it to run without DooM type graphics, do this:
1.) Set up the game type and tell it where the legacy program is, and then where "doom.wad" is located. Then click ok.

2.)Instead of clicking launch, go to single map, and select to start on E1M1. Then at the bottom where it allows for added maps, select the phase 2 beta 3 wad. Then click ok to automatically launch the game ^_^

It took me forever to figure that out.