Now that we have a specific answer from a dev regarding gear tiers, this might get cleared up, but up until now this is how i saw it:
No-Tier Items: all minor items that cannot be crafted. Examples: rubber boots, iguana-on-a-stick.
Tier 0: All items that can be crafted from level 1 with no training. Examples: tent, hatchet, Mauser.
Tier 1: all craftable items that require only pro training 1.
Tier 2: All craftable items that require blueprints.
Tier 3: Beyond blueprints. Examples: power armor, gauss pistol, pulse pistol, special CA*
Tier 4: Examples: HPA, gauss rifle, gatling laser, TPR, pulse rifle, Bozar, Vindicator
Tier 5: Examples: Advanced PA, Dual-Minigun Turret
Tier 6: Examples: Dual Laser Cannon Turret
Exceptions: according to this, minigun is tier 2. I call Avenger tier 3 since its a substantial upgrade, which means Vindicator is tier 4. Bozar tier 4. And because phazer is a Star Trek item (lol), its very nature puts it in max tier along with the alien blaster.
As for armor in TC, when i go with a 3-man team to do TC, and i wear Leather Armor Mk2 because i'm a sneaker, we can start the TC timer, but it stops soon after that. I have to switch to better armor and not be in Sneak mode for TC to work right.