Which world of Warcraft class can heal has high sustainable life and is very good at PvP
Some of the classes that match this description are explained below; mind you that the element of your personal skill can tip the favor towards one class or the other. Player preference does make a difference.
Paladin Paladins with a Retribution/Protection spec have reasonably high health, plate armor and can switch between a 2-handed weapon or 1-handed weapon and shield for additional protection or damage.
They can remove poisons and diseases from themselves and allies, heal by melee attacks and use Divine Protection, which makes them immune to melee damage for a short time.
Druid Druids can all heal and remove poisons and curses - but for the higher health totals you'd be looking at a Feral spec. Even if restoration specced, a Druid can switch to bear form to gain more health and armor, or to a cat form to stealth.
Druids can also immobilize enemies and the main benefit of their heals is that they can cast Heal-over-time effects, meaning they continue to heal while you take other actions.
Death Knight Death Knights are plate-wearers, and can have good health pools using any talent spec; however, Blood and Frost Death Knights will have the highest health.
The benefit of Blood abilities is that you gain a lot of healing while still damaging your enemies, and have a few on-demand health regains. Frost abilities are great at mitigating damage and resisting enemy attacks.
Priest Discipline priests have powerful shields and fast heals, meaning you have to burst them down to kill them. However, because they use only Cloth armor, this is also their only protection. Discipline priests are primarily for healing, so if your aim is to heal your friends while being very hard to kill, this is a good class. When primarily interested in going into battlegrounds solo, you are not going to be sure you will have reliable protection from the other people on your side and your damage is generally too low to kill PvP specced and geared players.
Shadowpriests are an offensive class with two varieties of Fear, which heal themselves as they do more damage. Like Discipline priests, their only real defense is their shield, but their Shadowform also grants them a flat 15% damage reduction. If you are interested in being able to heal in a pinch, but still able to deal damage, Shadowpriests are more balanced.
Warlock Warlocks are very versatile in PvP, being able to use different kinds of armor spells to grant them increased armor or healing done to them. Their demons can control their enemies or serve as soakers and dispellers. Warlocks who are Affliction can heal themselves for a great deal by dealing damage with Corruption, while Demonology Warlocks can turn themselves into demonic tanks for a short while.
Shaman Shamans can heal and wear mail armor, making them a compromise between the Paladin and the Priest in this regard. However, their reliance on totems gives them relatively limited mobility.
Personal experience with the Shaman class is not very advanced, but it seems that Enhancement is the talent tree that gives great benefits in PvP and allows for more toe-to-toe combat and survivability.
Other classes Rogues, Hunters and Mages can be very good at PvP, but are not able to heal themselves on demand. Their health pools also will not be bigger than the other classes mentioned - so while they are valid PvP classes and overpowered in certain combinations with others, they do not fit the question's scope.
