The big problem is the two archetypes of locker room monster :
There's the "never nudes". These guys shower in their bathing suit, then when they have to change, they huddle into a little ball in a corner and quickly slip one thing off and another on (or use a towel to cover up even then). They're tense and nerdy and you don't want to be like them.
Then there's the way-too-comfortable guys that walk around totally naked for way longer than is necessary to do their business of changing. The worst of these is the old closet gay guys. They're usually 60+ , have a giant white bush that thank god has overgrown whatever cock they once had, so that they now just have an androgynous mound of hair (and yes, I have looked at old man bush, you can't really avoid it when they come up to you and talk to you when you're sitting down and they're standing completely naked; okay old man, you got me to look at your bush, now go away).
So you have to try to straddle the line between too much showing and too little showing, which creates the painful awkwardness. The ideal man should not be afraid of anyone seeing his naked body, but he also shouldn't inflict it on those who don't want to see it, nor should he make himself the eye candy of perverted old locker room prowlers.
Shower? Definitely bathing suit off. On is way too anal. But mostly facing the shower head. Occasionally turn around to face the room just to show that it's no big deal. Only the absolute minimum of penis cleaning. But don't avoid touching it altogether either.
The walk to the locker is a difficult moment. To wrap the towel or not? Less than twenty feet away - no wrap. Twenty feet or more - wrap.
Dressing - reasonably quick to get the underwear on, but not a frantic dash. Don't stand in a corner, but also don't face the room.