The armour you'll wear will depend on how you set your character up. Burden is important for combat, so many thieves eventually don't wear armour and just rely on dodge. But before you have good defensive skills, or if you use parry, a set of lightweight armour can be terrific.
Detailed armour tables can be found on the main Discworld wiki: Armours
For the lazy, one set of lightweight armour looks like this:
- Set of overalls
- Padded monk's robe
- Laced-up leather breastplate
- Peaked cap
- Leather bevor
- Laced grflx leather jerkin
N.B.: it's fairly important to have armour enchanted, as that greatly increases the effectiveness and durability.