Warrior is going to rely upon a good two-hander. Hopefully, you should have received your Whirlwind Axe by now (look it up on google).
Take my advice as an opinion and not as a fact as you wish, but what worked for me in leveling and dungeons:
Arms Warrior is still a viable and strong leveling spec for warriors. Yeah, I heard two-handed fury works, and suppose if it’s a matter of preference… It can work as well.
Rend and Sunder aren’t as viable and mandatory as they use to be, especially at your level. You can use Heroic Strike above at 60 rage, but most importantly you can use that rage on Demoralizing Shout, Pummel and ThunderClap, ect. Leveling isn’t just about doing high damage! In my experience, I just learn to conserve my rage and barely use Execute unless the mob is about to kill me. Literally. Note: Well, I also do like to Mortal Strike on cooldown.
In terms of dps output, I have found the highest in berserker stance. Whirlwind is an absolute monster… and I mean an absolute monster especially paired with a whirlwind totem/shaman. Try it yourself against 2-3 mobs, and you will have a WAY bigger significant dps boost than overpowering/stance dancing. The only time I got outdps was by a shaman with 3-5 leveling epics, 3 elixir buffs, and a Dragonslayer buff. Whirlwind should not be a filler, but an off-cooldown priority especially against more than 2-3+ mobs. The damage is way too good to be denied. Believe me on this.
I also still use execute when targets get really low, and usually when there are only fewer than 3 mobs left. Otherwise, the next priority after Whirlwind is Cleave. Yeah, Bloodrage should be off cooldown and I also like to pool rage for my Deathpact. Some moments, you will have conserved your rage for Whirlwind, and some moments you can be aggressive enough to use use a plethora of damage abilities like Cleave and Mortal strike. Again, this will depend on how long the mobs will live and how many mobs will be left.
Also, a simple tip way to transition from Battle Stance to Berserker Stance is with a charge to begin combat initiation. If you switch to Berserker Stance midway during your charge, you still can able to retain more rage due to auto-attacking during that stance.