I think if you are learning anything you start with basics. To me Holy Priest has the most basic set of healing spells. You have flash heal and heal for starters. Those are spot heals. You also have renew. And to be honest, you could probably get away with just using those three spells while learning, and you would be fine.
Once you have those three down, then I’d say start using the other spells.
If you wanted to play disc and only disc, this is what I would do, and this is how I learned the newer disc playstyle. That is, the playstyle after atonement was introduced:
I’d make a level 1 toon. Then I would gear it with BOA gear that was enchanted. Then I would heal dungeons all the way up, learning to use the spells one by one as they were added as you level. That way you do not become overwhelmed, and because you are well geared, mistakes will not be detrimental.