Now, myself personally thinks that it should be down there in the bottom of the screen along with the Health, Armour and Ammo stuff, as it would fit best down there. As my Diagram explains:

(Please don't mock me for my MSpaint Skills, it was done in 2 minutes)
I know some people would argue it to be in a top corner or something, but this is the point of the thread, to Discuss it.
Now, the mapper will have to set entities down to add things to this log. The log could also perhaps Tick/Line off objectives that are completed. This would take up about 5 minutes of the mappers time to do, but at the end of the day, it helps this mod be more unique and better than other mods. It could also perhaps have a map of the level incase the player gets lost even more, though the map could show areas where the player has been and places they could go.