I'm following these instructions:
http://www.oblivionmodwiki.com/index.php/FCOM

At the section for Martigen's Monster Mod, it says that these files need to be placed in the Data folder: MMM.esp, Martigens Monster Mod.esm

In the archive, there are "Mart's Monster Mod.esm" and "Mart's Monster Mod.esp". It is referring to the same version of the mod so that worried me a bit. Took those 2 anyway, assuming they were the right files. But after finishing my FCOM install, BOSS said:
Mart's Monster Mod.espVersion 3.7b3p3
ERROR: Delete. Not needed with FCOM.


So now I am doubting both of the files. I am guessing I should delete the Mart's Monster Mod.esp as BOSS says, but what about the .esm? Delete? Keep as "Mart's"? Rename to "Martigen's Monster Mod.esm" or "MMM.esm"?

BOSS is correct. You do not need the Mart's Monster Mod.esp with an FCOM install--the FCOM.esp handles all that.
You DO need the .esm--leave it named just as it is.
I think you're getting confused with renaming the Mart's Monster Mod.bsa, which you should do to ensure that it loads. Make sure that you have that .bsa downloaded and placed in your data directory, and then rename it according to instructions.

Don't follow that guide. Follow the guide in the latest FCOM topic here, that's completely up to date.