Angel of Demons
"No random levels here! Starting at the Entry Base, you'll descend from one special level to the next until finally arriving at the Phobos Arena. You have to complete all of them, too!"
The idea here is to play a game of DoomRL with nothing but the 11 red-stairs levels, Base Entry, Hellgate, and Phobos Arena (and maybe HF if you want). The order would be according to the first level of possible appearance, like so:
Base Entry -> Hell's Arena -> Chained Court (hard) -> The Wall -> Hell's Armory -> Halls of Carnage -> Hellgate -> Unholy Cathedral -> City of Skulls -> Spider's Lair -> The Vaults -> Mortuary -> Lava Pits -> Phobos Arena(HF)
Stairs won't appear until the level is complete, meaning you have to go through every one. Alternatively, you COULD try to exit all of them and such, but it'll make killing the Cyberdemon basically impossible. (The only possibly without completing a level is the nuclear BFG, which could be changed around if necessary.)
Since some of the levels are (virtually) impossible without some help, you'll get some. Combat knife will show up at the end of Base Entry (like in AoB) for players wanting to melee, a couple envirosuit packs will appear at Lava Pits entrance, stuff like that. (As for UC, there's a new consumable that would at least allow for the possibility to win without investing in Bru/Ber.)
Due to completing every special (something a lot people may not accomplish until far later in their playing) I'd set the bar pretty high to attempt this, rank-wise. Need at least a few Golds, probably.