Depending on the class there's 2-5 must have skills for them, excluding passive stat-ups and HP/TP up skills. here's what I recommend:
Medic - Immunize and Salve 2 must be maxed out, no questions asked. You can also go with a maxed out Cure 3. it's a good grinding skill, especially for early on in the game before you face monsters that hit multiple people. way later in the game you can rest your Medic and redo them so they have maxed Immunize and Salve 2, and level 1 Revive (anything more is a waste in this skill) and then go for Caduceus to allow your Medic to do more than sit in the back row and defend.
Protector - mostly passives here. All you really need is level 5 in antifire, anticold and antivolt, and that's only if you want to do some optional bosses after you beat the main game. Otherwise? Just learn smite and invest in HP/TP/Def up and shields so your protector can take a lot of hits.
Survivalist - Apollon and Multihit are the attack skills you want. Trickery is a useful debuff. 1st Turn is really useful late in the game, but not so much for the first 20 floors of the dungeon.
Alchemist - poison is good for the first 8 floors or so. But I would just go with a fire/ice build instead, or you could go fire/volt and add in ice later. The best spells of the 3 elements are as follows: Flame, Freeze, and Thor. Thor is the 3rd tier spell, which does less damage to each monster than the 2nd tier, but hits all. There are more common enemies weak to thunder than fire and ice, but Flame and Freeze are worth it for those enemies that have a lot of hp/defense and are resistant to thunder. You also probably want Scavenge, and maybe a point into Warp too.
Landsknecht - decide if you want to go swords or axes. Axes kill single targets easily, swords clear out groups easily. If you go axes, learn Crush and Silencer and Hell Cry, and put the rest into ATK/HP/TP up. If you go swords you have to learn 2hit to unlock Allslash, and you may as well also get some points into TP up and unlock the "chaser" skills that automatically trigger after the enemy is hit with elemental magic (which makes them a natural pair with the alchemist). In that case the best one is Shocker so you hit all enemies twice when your alchemist uses Thor, but truth be told, Allslash does the job just as well.
Ronin - Overhead stance and Midareba. After you've maxed those, get some HP/TP up, and you may want to learn another stance or learn Kesagiri. If you take another stance, pick the one with the instakill strike since it's useful for an optional boss.
Dark Hunter - decide on whips or swords. If you go whips you will spend virtually all your skill points on maxing out all 3 binds, Ecstasy and Climax. Anything left over goes into HP/ATK up, since Ds get a ton of TP and don't need TP up. If you go swords, max out Drain and then choose Petrify or Nerve and max that one out, or max out Bait. And learn some Boost up along with the HP/ATK up combo.
Hexer - binds, relapse, and their sleep spell. I never really used one because they are so limited and specialized, but those are the skills all the guides/players say to look at.
Troubadour - saving the best for last here. Max out Relaxing and Bravery, fuck the defensive spells like Shelter and Mercury. Those are for cowards. Bravery boosts everyone but your alchemist's damage, and relaxing gives a huge bunch of TP regen. Best of all, these songs don't need to be refreshed like other buffs, unless someone dies and you revive them. To enhance their utility, learn level 1 blaze/frost/shock to give your melee guys elemental damage if you come up against someone with high physical resistance. edit: I forgot, you should also learn Erasure. level 1-5 is fine. Troubadours have tons of skill points to go around since they only need to max out relaxing and bravery, so just decide how many of the enemy's buffs you want to erase at once. I went with erasure 5 just so I could be a bastard, plus there was enough room for me to max out HP/TP up and all the other songs I needed along with it.
If you just want to maul the main game I'd recommend Landsknecht, Protector (or another Landsknecht), Survivalist, Troubadour, Medic. The T will use relaxing/bravery and buff everyone's damage/tp regen, the medic will heal, the landsknechts will tank and slaughter with allslash or axe skills, and the survivalist uses apollon and multihit to own bosses/FOEs. Alchemists don't suck in the main game by any means, but they don't really come into their own until you get postgame gear + run into the insanely physically resistant guys in the bonus section of the game. at least IMO. I used an alchemist early on and dropped him for a Landsknecht before facing the second stratum's boss, and never looked back.
. Also do I need Alchemist?