1) I know it's cliche, but "leap" was what made barbs playable for me. "dash" (don't remember actual name) is close, but can't span gaps, nor get over big bosses at times...
2) Even stock, I don't think any 1 skill (even SE) is "must have".
What I'd love is skills that don't require so much spamming. If I want to spam I'll play a summoner or spellcaster. Make the buffs "reserve" huge permanent chunks of available mana, adding strategy about "+mana items for more simultaneous buffs, or more normal type gear?" rather than just "spam buffs, spam mana pots, attack twice, start spam sequence again", like it is now. I want to concentrate on the beating, not the buffing.
3) I prefer a balls-out "freeedommmmmm..." approach, myself. Winning the arms race and keeping the magic 1-hit kill for as long as possible is my favorite part. Especially since it requires a different approach vs. bosses, which makes the gameplay more varied.
In a more general light, I'd like to see a real tradeoff between dual-wield, sword 'n board, and 2-handers. It would be nice if more skills used attack speed, not cast speed, and also if more skills took advantage of leech. As it is, most skills depend on DPS, so every approach gets you to the same spot, or else there's one clear "best" approach, rather than a speed/strength tradeoff.
Something like a cast skill that inherits your normal weapon attack speed, for example. "Devastating" with dual daggers, could be ultra fast, but with almost no range so you have to go right through the group of mobs. "Devastating" with a polearm might spaces out the attacks so that you're briefly vulnerable, but has much higher range so you can keep some distance and go _around_ the group instead. Some skills could of course still rely on DPS to keep both paths viable and balanced.
What about speed/armor tradeoffs? If you're wearing plate and carrying a shield, your "fast" skills and attacks will slow down, relative to wearing lighter armor types and only single wielding.
For tanking, you could try defensive skills that rely on facing, so it's not just a boring "I'm invincible now", but you still have to worry about positioning, similar to SE's current AOE. This would have the added bonus of tension between getting up close and dealing the damage vs. not letting the mobs actually _surround_ you.
Lotta quick, easy dreams on my end. Now get to work and make 'em happen!