Cleric Visible Armor

Which order should I be trying to obtain these in? From most to least important.

Whichever piece is the biggest upgrade over what you currently have in that slot.

Are you playing live or TLP?
Just make sure to uppgrade your heal and beneficial haste focus first. On live we have beneficial haste on boots and Heal on the Neck. Then you can pick to uppgrade your spell range focus from mask and beneficial duration from cloak.
If your Focus are covered, just do what Velisaris_MS said!
Good luck.

Live, thanks

For visibles I always tried to go Chest >> Legs >> Arms >> (Helm or Feet or Hands) >> Wrists.

Boots first, if you dont have the latest beneficial spell haste focus.
Breastplate next for the total stats and remedy focus and click effect.
1x Wrist next for the Chromatic damage focus (particularly since they changed our interventions)
Then just for stats, as the rest of our relevant foci are on non visible slots:
Legs
Arms
Head
Hands
Wrist2