Do we need to build and pay for an item only once

It's true for weapons and armor not built at the Proving Grounds.

It's not true for utility items and weapon-attachments, and anything built at the Proving Grounds.

When you build an item in the Proving Ground, you only get 1 copy of it each time. So, for example, if you want to equip your entire squad with any of the following types of armors:

1. Spider suit
2. E.X.O. suit
3. Wraith suit
4. W.A.R. suit

then you'll need to build one for each soldier.

Weapon and class items built in engineering only need to be purchased once:

1. Rifles (Specialists and Psi Operatives)
2. Gremlins (Specialists)
3. Psi Amps (Psi Operatives)
4. Shotguns (Rangers)
5. Swords (Rangers)
6. Cannons (Grenadiers)
7. Grenade Launchers (Grenadiers)
8. Sniper rifles (Snipers)
9. Pistols (Snipers)

Medium class armor can also be purchased once for your entire squad, unlike the light and heavy armors from the Proving Ground:

1. Predator armor
2. Warden armor

All other items built in engineering will only give you 1 new copy for each purchase.