I think it depends on what you mean by "best". If you mean a collection of skills that would offer the best possible outcome, I'd just go for 5 CC heavy skills that would allow you to stun-lock an opponent (Gold Card, Dazzle, Cryptic Gaze, Counter-Strike, and Fear would be a pretty solid line-up there). If you go by categories of what the skills accomplish things get funner though.
Best offensive skills:
1 - Minion Farming: Karthus's Lay Waste (solid range with minimal cost)
2 - Skillshot Harass: Nidalee's Javelin Toss (#1 Aram terror because of this)
3 - Single-Target Nuke: LeBlanc's Sigil of Silence (lots of assassins have a solid burst skill, this one just seems slightly better than the rest)
4 - Multi-Target Burst: Fiddlestick's Dark Wind (team-wide silence, bounces can hit the same unit multiple times)
5 - Auto-Attack Steroid: Vayne's Silver Bolts (can't go wrong with % true damage)
Best Defensive Skills:
1 - Anti-Magic: Morganna's Black Shield (CC immunity helps. A lot. Nocturns and Sivirs are K, but not team-freindly. Sivir's also has a retarded 0.5 second delay)
2 - Anti-Physical: Jax's Counter-Strike (Pretty much defines him as the champion that will win against anyone even remotely reliant on auto-attacks).
3 - Sustain: Soraka's Astral Blessing (outclasses all other non-ult heals in the game)
4 - Escape: Shaco's Deceive (Flash with stealth, can't go wrong there)
5 - Troll: Fizz's Playful/Trickster (Like Vlads, this moves you places and slows enemies. Unlike Vlads, this one is easier to juke with and doesn't cost health).
Best Utility Skills:
1 - Gap Closer: Kha'Zix Leap (Not sure how you feel about usaing an ultimate to upgrade a regular ability - but upgraded this is almost better than Kassadin's ultimate with comparable range - beyond that it's a skillshot leap rather than targeted, so good for escaping and initiating. Re-set on kill or assist to).
2 - Team Buff: Jayce's Acceleration Gate (free Shyrelia's with a lower cooldown)
3 - Single-Target Crowd Control: Fiddlestick's Fear (what it lacks in damage it makes up for in never missing, and having a short cooldown)
4 - Multi-Target Crowd Control: Alistar's Pulverize (what it lacks in reliability it makes up for in being un-mitigatable by tenacity and capable of striking in an AoE).
5 - Displacement: Blitzcrank's Grap (Probably the best non-ultimate in the game. No gap-closer necessary to jump in the middle of 5 enemies, you bring the enemy to your 5 man team).