Trying to gauge how much emphasis or resources I should place in attempting to raise my characters' AC. Understood that getting to a 20 (or 20+) is obviously a goal. Nor am I suggesting to turn down options to increase an AC if offered. The purpose of this exercise is to gauge the value of gaining another +1 oppose to some other benefit. For example, dropping your AC from a 17 to a 16 but gaining resistance to a damage type; or if the value of gold between a +1 and +2 armor is better used  for another magical item. 

So I will generalize roles below. The input I am looking for is the line were increasing by another +1 should not be a priority. If it helps, ask a question like "you can spend additional resources to increase a weapon/gain resistance/access a feat/execute spell or increase your AC by 1."  Identify the line where adding to AC is not nearly as beneficial as increasing some other attribute for the character. 

Frontline fighter: This your tank, shield, damage dealer, etc. 
Thrasher: This is melee damage dealer who supports the frontline. Examples are a rouge who comes in to sneak attack, a player who can land good damage and avoid being the focus of enemy attacks, or a character who rushes in when an enemy is damaged to lay in attacks for the late rounds. 
Range attacker: Keeps distance from the main action. Only engages in melee combat if the enemy makes the effort to approach, or if circumstance places them in close combat.
Battlefield Tactician: Probably a synonym for spell caster, but the difference between this and the range attacker is the battlefield tactician is a far as possible form the action; and that includes artillery of the group. They may even use actions to distance themselves and saving their influence in combat until the next round. 

Thank you for your input and discussion. Feel free to add in more topics for discussion. 

Cheers!

The simplistic answer is that a frontline fighter will want it as high as possible, others need it less.

The more accurate answer is that there is no universal answer. A long range caster will still love AC because it helps their low HP stretch further and makes it less likely that they'll have to do the dreaded concentration saves. In a campaign with plenty of healing or lots of save-or-suck spells, a frontline fighter might not even be all that bothered about AC and will concentrate on other aspects like Dex and Wis to be resilient to the saving throws. Two of the melee classes (one is designed as THE tank class) has a central feature where AC generally maxes out at 20 - other classes can often get this beat at around L5. That wouldn't be true if AC were universally important to frontline fighters.

So, how important is AC? An increase of +1 to your AC means an 5% of all directed attacks (IE not based on saving throws) will be deflected. That's all we can really say in the general sense - whether that's important to you enough to sacrifice other gains really depends on your tactics and strategies, how you're building your character. To be honest, even your combat role is only roughly correlated with the importance of AC.

That kind of answer isn't as satisfying as I'd suspect you'd like. However, you've demonstrated enough understanding to know the kiddy lesson "AC is awesome and will keep you safe" and you're ready for a more holistic and honest answer.

How much you should invest in your AC depends on how you fight and what tactics and strategies you're employing in order to be meaningful on the battlefield and to survive it.

fighters, around the maximum someone can get... about 25.
monks and barbarians, about what maximum stats can get them. thats about 20. 10+5con+dex for barb and 10+dex+wis for monks.
wizards are an entirely optionnal thing, they can literally wipe out the bounded accuracy of the game getting a whooping 36 AC and becoming practically the only charcater able to fight a tarrasque in the face !

mind you these are all without magical items...
with magical items, pretty much everyone except wizard can go up to 30, with wizard getting near 40 making even a tarrasque unable to hit without a crit.

if you ask how they get ?
robe of the archmagi gives 16+dex at max level thats 21 AC the equivalent of a +3 full plate for a fighter.
bracers of defense gives another 2 AC. bringing them to 23.
ring of protection +1 or cloak of protection +1 or ioun stone of protection +1. thats 24.
blade singer adds intelligence bonus... at max thats another +5. making it 29.
the shield spell brings it to another +5. thats 34. the haste spell adds another +2 thats 36.
warding bond spell (cleric cast) +1 --> 37 ac, Shield of Fate (cleric cast) +2 thats 39 AC.
for good measures, that wizard cast mirror image as well.

i am sure i am missing something to push through the 40 barrier. but i am not thinking about it right now.
basic without magical items or spells... you are looking at about 20 AC at low levels... about 23 to 25 at mid levels. and above 30 at high level.