I don’t think that you should use an embedded ditrobution.
I reccomend that you do a “Linux from scratch”. If you’re not familiar with it, it means that you download all of the components of the os(kernel, shell, compiler, basic tools), and install them 1 at a time. You choose exactly what you want. Also, since you compile everything from scratch, it runs very fast because it is optimized for the hardware.
I recommend, that you build the system on another pc, and then strip it down to just a minimal shell and X windows. Total, it shouldn’t be more than 70mb.
note: If you only want to run 1 program in X with opengl, then you don’t need a window manager. Just execute the program in your .xinitrc file instead of the window manager.
As mentioned, you don’t have to have a window manager but you could have keyboard focus problems without it. Your app may already handle focus in the absence of a window manager, if not look into XSetInputFocus.
The manpage for xinit has some discussion about .xinitrc
A couple of notes.
If you use the graphical login, you need to use $HOME/.xsession instead of .xinitrc
The script may have to be executable
If you mess up in the script it can be hard to log in to fix it. I suggest having a second login with permissions to edit/delete the .xinitrc or .xsession file until you have it right.
If you want to install a mininal X windows, then I think that your only option is to compile it from source. If you get a binary verision then it will probably contain hundreds of input and video drivers that you will not use.
About not using a window manager, just replace the line in .xinitrc that starts the wm to the program you want to run