Melee champs are good in ARAM. Don't get stuck in the auto lose mindset because you're "stuck" with a melee. Quite a few are gods in ARAM: Trundle, Maokai, Mundo and more.
Be prepared to die often as a melee. Your team needs you to engage so do it, try to engineer situations where you don't have to be a sacrificial lamb but always be prepared to die for your team.
The only champs who need CS over others are stacking champs, for everyone else its a freeforall.
KDA isn't very important so don't covet a positive one. The only thing that matters is who is alive to push and defend.
Do not wait to buy pen items. If their team has 2 tanks/tanky champs and your team is mostly AD or AP you will need pen sooner rather than later. Void/LW item second buy is not a waste of gold, you need them to break the frontline and stay relevant.
CDR is king quite often. Luden's/Zhonya's/Transcendence will cap you quickly and being a Lux/Ziggs/Xerath etc with 40% CDR allows you to own at least one side of the map permanently.
Take runes you normally wouldn't, particularly Presence of Mind. If my champ is mana hungry, regardless of type, I take PoM. Other runes that give things for free are also excellent choices.
Shaco is a bad ARAM champ, don't ever forget that. I've lost/won more ARAMs because of him being on either team than any other champ, even experienced Shaco's bring virtually nothing to the group and play selfishly all game.