Heals: Essential to most, if not all decks. An optimum amount of healing would be around 9-11% for a blitz deck, and 22% for a 'regular' superboss deck (one that has a balanced number of healers and attackers). It used to be that the more healers you had, the better, but with the introduction of more and more hard hitting bosses, harder quests now require you to be able to tank hits and clear fast. Still a very important component of any decks. New players should focus on getting at least two healer-emblemers of each colour.
Attack-based: Comes in many variants (unconditional, combo-based, health-based, attribute-based, etc.). LIke heals, these are part of the foundation of any deck. Unconditional multipliers are the easiest to activate, but most are not suitable for long-term use because their multipliers are very low. There are certain exceptions to this, of course, but new players should work on getting two hard-hitters of each colour, to build a balanced deck, before thinking of blitz/stall teams.
Fury/Variable Attackers: These would go under the attack-based category but they're so useless they get a whole category to themselves! Yay!
Trimagic/Undivided trimagic: Undivided trimagicians are good when facing more than one fodder, and will help you smash your way through a lot of stuff in the early-game stages. Divided trimagicians are generally undesirable, but can be powerful against a single boss. Not really necessary for any sort of deck, but most of the undivided trimagicians we've got are good for superbosses so there's really no reason not to use them. Tourneys are where these two skills shine. In a deck, undivided trimagicians go in front, and divided at the back. Pair well with attack boosts.
Split (consecutive) attack: Not good, not bad, for superboss quests. Amazing for tournaments (can save you a turn or two per round). Put them in the back, behind even divided trimagicians.
Team Boost: Usually look like this, "Increase ATK of [x] element members by [x] amount". Large is a 20% boost, Huge is 25%, Massive is 30%, Ultimate is 40% and Baron is 80%. Mid- to end-game skill. If you don't have the foundation of your team sort-of set, what's there for them to boost? Because of that, they aren't very good spirits to start with, but are worth investing in (again, there are exceptions like Isabeli, who's just ridiculous). In a deck with 2 healers and 2 attackers, a boost could be a candidate for the fifth spot. However, anything below a large boost is just a waste of a skill slot. Pair well with trimagicians, and are good for tourneys.
[The Wiki's List of Answer Skills]