Taric has three spells to choose from when deciding what to level. His first three points are going to go into each skill since they're all very good. The question is what do they gain from extra points?
Q: Imbue, the healing spell. Heals for 60 base on two targets for 80 mana on a 20 second cooldown. (Always Taric and someone else.) Extra points increase the healing done by 40, increase the mana cost by 15, and knock 1 second off of the cooldown. So it gets more mana efficient on top of providing better throughput.
W: Shatter, the flexible spell. An aura which passively increases armour by 10. Provides double that amount to Taric. Also gives an AoE attack spell which hits everyone around Taric for 60 damage and lowers their armour by 10 for 4 seconds. Costs 50 mana and has a 10 second cooldown. While on cooldown Taric loses his doubled armour but the aura remains. Putting a point into it adds 10 to the mana cost, adds 5 to all the armour numbers, and ups the damage done by 45.
E: Dazzle, the stunning spell. Ranged spell which stuns an enemy for 1.5 seconds. Also does 40 damage. Costs 95 mana and has a 14 second cooldown. Putting a point in lowers the cooldown by 1 second and adds 30 to the damage done.
Right away, if you're looking to do more damage you'd rather put the point in W than anything else. 45 damage is more than 30 and way more than 0. This is before taking the armour reduction into account. I've never seen anyone recommend leveling dazzle first and it just seems wrong unless you _really_ want to stun every 13 seconds instead of every 14 seconds.
Now, what does the armour actually do? I took a look and it seems typical armour values at low levels will be around 50. We're already giving 10 so we want to see what the gain for our buddy is when we take him from 60 to 65. We also want to look at the extra damage done to the other team when we lower their armour from 40 to 35. Also I guess relative to the base of 50 so we know what's going on when we're playing not-Taric.
Going from 50 to 40 (what happens when shatter is used with 1 point) is an increase in damage taken by 7.1%. Going from 40 to 35 is an increase of 3.7%.
Going from 50 to 60 (what happens when you stand near your friend with 1 point) is a reduction in damage taken of 6.3%. Going from 60 to 65 is a reduction of 3.0%. The healing spell heals your friend by another 40 damage. How much total incoming damage would they have to take for an extra 5 armour to prevent 40 damage? 2112 raw damage. That's not going to happen when you have maximum health in the 600 range. So if you just want to survive you definitely want to level the healing spell. Especially since it lowers the cooldown!
So it seems if you want to play defensively you want to level up your Q. If you're playing offensively you want to level up your W. What if you're somewhere in the middle? My feeling is that since the W does provide some defensive benefits and the Q provides no offensive upside at all that it remains correct to level W most of the time. Personally I want to play Taric offensively so there's no question in my mind what I should be doing. But now I know if we're falling behind in lane and we just want to turtle that the heal is actually better than the armour. Good to know!