When I healed in Vanilla, I used all the standard blizzard UI settings and possibilities.
Aka, i didnt have any mods, addons or anything, I wanted it simple, I only had threat meter.
I had all the groups displayed on the screen and I clicked the ones to heal if they are in range.
For the main tank i would just click on the character on the screen since he usually is in front of the boss alone.
I was always active unless my focus was the main tank then i didnt help anyone.
I would try and click all warlocks that were life tapping and slap a renew on them and try to save the rogues from getting annihilated because they wouldnt move from the cleave lol.
I was always on my toes and always out of mana at the end of the fight because i tried to do too much and save everyone and heal everyone even though we have other healers in the raid!
There were probably better ways of healing with macros and mouseovers but i had more fun clickings and trying to save everyone i didnt care
I had a shaman in vanilla and got to 12/15 naxx with it.
As others pointed out already, healing is basically 'whack a mole' in raidframes. I would say it's stressfull and simple, but also very satisfying, because you control who lives.
But sometimes you ignore all encounter mechanics, especially as paladin, so it's not suggested if you want to experience the raids in all mechanics.
So back then we tend to say you hide your weaker players in the healing crowd and for MC that is correct. But starting with Vael you need to deliver too and that is one of the reasons why raids are staying in the 'MC guild' tier.
Later, especially in Naxx or Deep AQ40, you need to be pretty skilled, because your raids wants/needs to kill fast and are bringing more DPS or Tanks, so the remaining healers better be proficient.
If your choice is healing, I still suggest going priest, because of spells like https://classic.wowhead.com/spell=10938/power-word-fortitude , https://classic.wowhead.com/spell=25315/renew and the reliable https://classic.wowhead.com/spell=25314/greater-heal . Shaman raid healing is later indeed different ranks of https://classic.wowhead.com/spell=10623 and a https://classic.wowhead.com/spell=16188/natures-swiftness macro for your assigned tank.
But if you want to have alot of fun supporting your group and always having the right tools, then shaman is the right choice.
For addons I strongly suggest every raid healer some raidframes with healcomm and proximity check like https://github.com/gnwl/NotGrid .