I have The Sims AnyGameStarter but it seems to not work anymore for some unknown reason. Used to work just fine. I get a missing shortcut error every time I try to run it now. Anyhow, I would just like to know how to create base compatible games without having to uninstall the EPs I have so that I can package lots and sims and pass them along to friends who do not have the EPs I have.

All lots will require whatever EP's you have installed, there is no way to make them base game without having an install of just that EP.

Sims don't require EPs except for their CC though - if they're installed with Clean Installer, they won't need any EPs and even if they use EP content, they'll default to base game stuff. So you don't need to worry about it for sims.

Try uninstalling and reinstalling the AnyGameStarter. As far as I know, it still works. That's how I make all of my base-game compatible lots.

Are you thinking about packaging occupied lots, or sharing lots and CAS sims separately? You should be aware that there are issues sharing occupied lots, unless they are properly cleaned. See this wiki article for more information:
Game_Help:Moving_Sims^wiki

I was originally going to do sims only but then decided that perhaps they might do better with a house--a very basic one containing just the bathroom and kitchen items, nothing else.

I have re-installed anygamestarter several times and keep getting that pesky shortcut not found message. Not sure what its looking for or where it went. The program just isn't working anymore. Worked great a while back when I installed it. I'll try the cleaner and see how that works.

I would think that the sims alone should be compatible.