What do you do?

I use ZDoom. I have all my IWADs in my ZDOOM dir. DOOM2.wad; DOOM.wad; Plutonia.wad and TNT.wad. If I run zdoom.exe - it'll run doom2. So I made .bat files for each game. ZDoom1.bat - move all IWADs but doom.wad - run zdoom.exe - and a zdoom2.bat and a zdoomtnt.bat etc. How do other people tackle this problem?

Zdoom (& many other ports too) has a command-line parameter (-iwad) that enables you to choose the iwad. I myself have many ports installed. Most of these use the -iwad parameter to read into the original DOOM directory. The original DOOM cannot use the aforementioned parameter, so I had to do something like you did when using doom(2).exe. but a rename command in the batch is much better than moving dozens of megs of iwad around (ren doom2.wad doom2.wa_, doom2.exe... ren doom2.wa_ doom2.wad, for example). In addition, you can also use response files (@myparams(or whatever).rsp) to ease changing the game, making notepad open .rsp files by default.

Why the hell don't you try my frontend ?

It was developed for such cases !

I downloaded it and installed it - I get run-time error 53 when I try to launch a DOOM 1 game - How do you warp to episode 3 mission 7?

It's possible that you are using a wrong port configuration (in the frontend). Default is pr/glBoom. There are some example config-files on my site.
If you don't know what to do, mail me your configuration (used port, e.t.c). I will create you individual config files to get the Baby running :-)