The only one I consider absolutely essential is Chrono Strike (time slows while you aim in midair - runs on a slowly regenerating meter). It makes life WAY easier for shooting out weak points while all hell is breaking loose around you. I found myself needing to do this a lot starting from level 2 and onward, and I swear I just plain failed a later room in level 2 on Nightmare because I didn't pick this rune first when I should've. I don't have the mechanical skill to quickscope and snipe targets at full speed, so I need this rune. Fucking arachnotrons.
I highly recommend the scope/sniper attachment on the assault rifle. I never used this in 2016 (who the hell wants to snipe in Doom?), but I like it a lot in Eternal because it's an easy hitscan way to shoot out weak points, and that's an essential skill in higher difficulties. I can't aim that damn shotgun grenade over long distances to save my life, and you need to make a lot of precision shots. This, combined with chrono strike, is my bread and butter for taking down weak points.
Other nice ones to have but less vital to get first:
- air control during jumps
- faster speed after a glory kill - I got this one first but it's not as vital as you might think. You're already pretty damn fast without it, and you have dashes too.
- Longer stagger times
- further glory kill distance
- one-time save from death if you take lethal damage
For suit upgrades (takes coins, not crystals), I highly recommend getting the faster weapon and mod switch first. The default swap speed is way too damn slow.