What is something you want to see in this type of game?
Honestly all I'd recommend is ensure the overall style and feel isn't simply a quake replica; art direction will go a long way here too. Personally I'd start with the weaponary as an example, maybe focus more on the arcane (since Quake's were very normal/techy) or some combination of two styles like that shotgun shown in the video with the... glyphs?
What is something you do not want to see?
Walking into a room, forced to backpeddle to gun them down, progress forward, rinse repeat. Common mistake I see in "retro fps" attempts. I'm perfectly fine being forced to keep on the move, area denial and such, but that's done through varied enemy types and properly designed encounters.
Art related suggestion
I understand its probably too early to bring up art related stuff, but I feel this is still worth mentioning so it can be thought about earlier than later in regards to, not only visual style but also gameplay;
Don't be afraid to get bold even with something as simple as ammo sprite pickups. I'm assuming those pixel shells on the floor are temporary, but do ensure even these item types look visually appealing and have distinctive silhouettes which can be recognised from across any room/distance, even if the item art needs to be larger than you currently have it. A few pixellated blocks will eventually be lost amongst the scenery I fear. Here's a
rough example I whipped together to showcase exactly what I'm thinking.