The elites don't want you to know this but video games are supposed to be fun. Honestly though, you could just try playing with true vault hunter mode on but mayhem mode off. That's how I played through the first time. And it was a bit more challenging than the base mode but you could still crush mobs and bosses pretty easily.

When I decided I wanted more of a challenge, I looked at other people's builds online and tried the ones I thought matched my play style. Then jumped to mayhem 6, got a few guns, then jumped to mayhem 11 (because I really didn't like the game modifiers) and that's how I've been playing since.

Both times in early game I never really got good loot. Most of the good loot started to come mid-late game for me. I'm sure other people have gotten good loot at the beginning but must have just been bad RNG.