If you really want to minmax this, the best way to do it is to figure out the incremental cost of each point of AC from any given source, budget a certain expenditure for AC, and calculate the best available AC for the budget.
I'm going to operate on the assumption that you aren't cheesy enough to try to claim both a sacred and profane bonus to AC on the same character, and that you're limiting yourself to the AC boosts actually described in the DMG (armor, shield, nat armor, deflection, luck, sacred, and insight, plus stat mods). I'll also ignore, in the analysis, any secondary effects that might make stat boost items more attractive than comparable AC boosts from other sources. The costs assume all bonuses are slotted and at standard x1 cost multiplier. You can create your own tables of costs per point of AC if you apply the cost multipliers to certain bonuses.
The incremental cost for an armor item (such as bracers of armor) is as follows for the first 8 points (non-epic):
1000 gp, 3k, 5k, 7k, 9k, 11k, 13k, 15k
A shield bonus is hard to come by for a monk, since shields really screw up their abilities. However, if the DM allows it (and you're the DM, so why not?) you can create an item with a permanent shield spell for a 4 AC bonus and a cost of only 4000 gp. Off the charts cheese, but that doesn't seem to be an issue. I've also neglected entirely both polymorph type magic and the option to pick up a permanent reduce person spell. Reduce person is one of the cheapest AC bonuses you could get (2 AC for 4000gp), but really pretty useless given its effects on offensive ability.
Wisdom and Dexterity enhancers have incremental AC costs of:
4000 gp, 12k, 20k.
Wisdom and Dexterity inherent bonuses have incremental AC costs of:
55k, 55k.
Deflection and Natural Armor bonuses cost:
2k, 6k, 10k, 14k, 18k.
Insight, Luck and Sacred bonuses cost:
2.5k, 7.5k, 12.5k, 19k, 22k.
A Haste bonus (based on permanent haste item) costs:
120k.
A Monk's Belt costs:
13k.
Your standard 16th level PC has 260k to throw around. If you budget 100k to AC, you would come up with:
Shield spell item (4k, 4AC)
Armor item +6 (36k, 6AC)
Natural armor and Deflection items +3 each (36k, 6AC)
Insight, Sacred, and Luck items +2 each (30k, 6AC)
Wisdom and Dex items +2 each (8k, 2AC)
For a total of 104k spent and 24 AC, giving a total AC of 34 + base Wis and Dex mods. Around a total AC of 40-42 for a monk with good stats.
With a budget of 165k you would increase:
Wis and Dex items to +4 each (24k, 2 AC)
Sacred, Insight and Luck items to +3 each (37.5k, 3 AC)
For a total of 165.5k spent and 29 AC (total AC 39 + base wis and dex mods).
If you want to blow most of your budget on AC, you would add:
Monk's Belt (13k, 1 AC)
Armor Item to +8 (28k, 2 AC)
Deflection and natural armor items to +4 (28k, 2 AC)
For a total of 234.5k spent and 34 AC (total AC 44 + base dex and wis modifiers)