Are barbarian health regeneration options limited to health potions and the occasional magic item that restores health at x per second?
No, since the Barbarian will be one of the main classes to choose when you want to play a "tanky" character, there are a lot of ways to get healed:
First, there's the templar. He has one ability that can flat out heal you, and one that can intercept enemies and heal the attacked player when you're at low health.
Second, there are item bonuses that grant life-leech, as a flat bonus or % of damage done, and also items that increase the amount of healing you receive from orbs.
Third, some skills of the Barbarian offer health restoration or regeneration. They are:
- Frenzy with Triumph Rune: Each enemy killed by frenzy restores 8% of your max health over 8 seconds
- Rend with Blood Lust Rune: Gain 9% of the damage done as health.
- Whirl Wind with Blood Funnel: Critical hits restore 1% of your max health.
- Ignore Pain with Ignorance is Bliss Rune: Gain 20% of all damage dealt back to life while the skill is active.
- Anciet Spear with Dread Spear Rune: Gain 60% of the damage inflicted back to life.
- Revenge: Heals 5% of your max life for each enemy struck.
- Revenge with Vengeance is Mine: Heals 8% of your max health per enemy struck.
- Furious Charge with Dreadnought Rune: Heals 8% of your max health per enemy struck.
- Overpower with Revel: Heals 8% of your max life for each enemy hit.
- Battle Rage with Swords of Ploughshares Rune: While the effect is active, critical hits have a 5% chance of making enemies drop health orbs.
- War Cry with Invigorate Rune: Increases your max life by 10% and also regenerates 310 Life per second while the effect is active.
As for "best", this is of course, situational, since you unlock some of these runes really late in the game (above level 50), but assuming that you have access to all of the runes above:
- Rend with Blood Lust Rune: If you have a lot of enemies around, 9% of damage done back to you should keep you at full health all the time, even for heavy hitting enemies.
- Ignore Pain: This skill in itself protects you from damage (65% for five seconds), so this should be the optimal skill to use if you get in dangerous low-health situations and need to heal back up. In combination with the skill above, you practically shouldn't die to anything but champions or named monsters, ever, and even they should have a hard time.
- Revenge with Vengeance is Mine Rune: 8% of your max health back is a lot, especially since (in my experience) Revenge seems to trigger quite a lot.
- Furious Charge with Dreadnought Rune: Not only does it heal you 8% per enemy hit, it also enables you to actually get out of dangerous situations should you ever happen to be surrounded (it happened to me and I tasted death :P )
- Overpower with Revel: This skill is instant and easy to use. It has a relatively low cooldown, but it can be lowered by 1 second if you strike a critical hit. This should prove especially useful later in the game, when you have some critical strike gear.
Those are 5 skills, you'll still need to bind something to your left mouse button so you can always use it. Frenzy is perfect here, since it's a great rage generator and also heals you with the Triumph Rune.
As a sidenote: I discourage the use of Ancient Spear with the Dread Spear rune: The damage it inflicts isn't a lot, at all, meaning the healing you'll receive is tiny. Plus, in higher difficulties, in situations where you need the healing, you'll want enemies away from you, not near you.
Ancient Spear with Dread Spear Rune: Gain 60% of the damage inflicted back to life.
Used with the passive No Escape: Increases the damage of Ancient Spear and Weapon Throw by 10%. In addition, a Critical Hit with Ancient Spear resets the cooldown while Critical Hits with Weapon Throw have a chance to return 14 Fury.
This combination with a 2 handed weapon has the potential for the most healing done at once, in the Barbarian class. Gaining 60% off a 200,000+ crit, multiple times, is a lot of health. The drawback is that you need to score a critical hit and gear/damage plays a large role in the health returned.
Life on hit. You can get it from amulet and rings as well as weapon. Then use cleave instead of bash. If you have 1.5 - 2k life on hit and you hit 3 enemies on each swing, you are replacing a good amount of hp every swing. Much more than you will get from % life leech on inferno because % leech is nerfed on levels above normal (only leeches 20% of stated amount on inferno). So if you hit for 20k with 5% life leech on inferno, you only recover 200 hp per hit, and you can get way more from life on hit.
In addition to the skills heishe listed, items with life leech effect are a great source of self healing.
Equipment can grant a flat amount of health per hit, or, better yet, a percentage of the damage you deal. Considering that you should be doing nearly constant damage, this adds up, and if you can stack some of the better values from items, it will add a lot to your health pool.