Breaking down the class in detail, paladins can fulfill all three roles in the game - damage dealer, tank, and healer. Retribution is the damage dealing tree, being a melee-range DPSer, dealing a mixed damage of physical and holy type. It also has some built-in sustain from Art of War. These things combined make the tree the fastest and easiest one to use for leveling. Protection is the class's tank tree, having significantly lower damage, suffering from mana issues until you get Blessing of Sanctuary and Divine Plea. It can handle multiple enemies with ease though, as it is quite sturdy. Holy is the tree used for healing - it has superb sustain, of course, and the strongest single-target healing in the game, but its damage, and thus leveling speed, is horrible and it should only be used if you're pairing with one or more players during leveling.
Regarding Holy's utility, Beacon of Light allows you to keep healing the main tank while also healing the group, as paladins have no area-of-effect heals. Aura Mastery, if used properly, can mitigate a significant amount of damage. Usually you will run with Concentration Aura in groups, which will reduce spell pushback for both healers and damage-dealing casters. Apart from that, they also have more liberal access to the rest of the supportive paladin spells, called "hands". Mastering the class revolves around mastering the use of these "hands", which makes the difference between an average paladin and a really good one.
Actually taralej I believe a shaman's Healing Wave hits harder than a Holy Light, so we're not the best single-target healer. We are, however, the most efficient tank healers in the game.
Oh and..
1. Yes. None of the healer specs of any class can really kill someone.
2. Holy Paladins are primary tank healers, having extremely efficient and huge single-target heals.
3. Two-handed, as you're focused mainly on damage. Crusader Strike and Divine Storm both deal % weapon damage, so 1h Ret is not an option.
4. Keep doing the chain quests and raise your rep. Tranquillen rep will give you a nice 2H sword for start, and then you'll get a nice two-handed sword from the Deatholme chain.
Thanks! It is very helpful and informative. Another round:
1. How they fair in survivability in terms of PVE and PVP?
2. Since they are big single-target healers as you've said, does this mean they don't offer much utility in a PVP setting? Since most of the time it's group vs group? (Sorry I have no idea in WOW's pvp world).