VATS accuracy is dependent on Perception which will allow you to hit an opponent with your weapon.
VATS usage is dependent on Agility which allows you to do more actions with your weapons.
Filling the critical meter depends on you using VATS (this is the fastest way at 5 to 10 attacks and kills seem to fill it more. I don't know how its calculated), moving (not yet proven), normal attacking an opponent.
Critical damage can improve from many different factors including your weapon, your perks (mostly luck based perks) and your stats (mostly luck). If you have all the perks filling up the critical meter is easy and you can also bank up to 3 critical hits.
Critical attacks can only be done in VATS (spacebar in PC or square in PS).
Sneak attacks can be done both inside and outside VATS (I prefer this method).
Early game this will be hard to do even if you maxed out your Luck and Agility stat first and went from there. You need Perception to hit your opponents for filling the critical meter. You need the Agility to do the actions. Without those it will be hard to kill an enemy let alone hit them properly unless you fight without VATS first then when the meter is filled up you go into VATS to use the critical.
You will have to be very good at evading attacks and attacking from a distance if you go the route for critical first, then the other perks and stats.
In conclusion: Luck perks are better for critical damage but you won't have much damage without Perception perks. So go for Perception first and add a couple of Luck along the way for improve critical damage. Unless you are doing a melee build then you also need Strength for that.