I've got two early approaches to leveling my character when it comes to nightmare.
I try and build towards a trait set that lets me kill imps or weaker in one shot most of the time (EE + Chaingun, SoB + Combat Shotgun, Shottyman + Shotgun). Important to farm a little ammo in the early levels with this idea, cause you're basically counting on your ability to waste the resurrected enemies in quick order. I found that mixing up Fin and SoB, Fin>SoB>SoB>Fin... really gets more efficient than focusing on one.
Or I try to maximize my speed with HR and then move on to more utilitarian traits (HRx2>Shottyman, HRx2>WK, HRx2>Berserk) which won't take enemies out before they can act but mixed with the additional speed will build towards something specific, like Blademaster or Fireangel (cause those Viles/Mancubi/Revenants are just that much more deadly. The sooner you are moving quickly the fewer enemies you have to fight. Pray for Malek's Armor ;)
Leaving powerups for later is also not the best idea. If it's located somewhere you've got to return to (like near the exit) you might leave it be, but take a peek at the layout and see how many dead enemies you'll be seeing again on your way back. Usually you're better off grabbing it. And if you see one in a new room and decide you won't be coming back for it then run! You've got to abuse running when you enter new rooms, especially if you see a powerup that'll let you remove tired.
I'd suggest never picking up powerups until you're tired. Always hit run, just to train yourself, before getting that status restored. It'll save you health from lurking enemies, time with bonus health (which happens more often with the doubled powerups), extended invulnerability, and destroyed powerups from splash if you can get to them a little faster or those caco's miss you while you're standing next to it.
And lastly, explore the room thoroughly. Just cause you need the speed doesn't mean you should find out you passed the stairs half a level ago and every demon and it's mother is going to get a second crack at you.