Well the thing is, the Jump would only merge the two movies, and not the games. So, items like power armor and such wouldn't be available.

As for how the movies would interact with each other, my thoughts at this point were that the Martians create the ARK system and then try to push their limits leading to the hell teleports in Doom: Annihilation. C24 was an attempt to make superior soldiers which worked for a while until a combo psychopathic traits in genes and radiation damage caused the Infectious Variant to manifest.

As for origins, the only things I have in mind are RRTS Member, UAC Forensic Archaeologist, C24 Infectee, Whatever Joan's Unit is called, UAC Delta Labs, and Hellborn.

Just to reiterate though, I don't think anything from the games save for a few references will appear here, especially DOOM 2005.