Aha! This is just the kind of question I can answer.

So firstly, it depends on what your role or social background was.

The Portuguese employed two general types of troops in the east: Fidalgos who were nobles, clad head to toe in an expensive full set of armour, who were often at the top commanding positions, and also formed the veritable "spearhead" of assaults. Most notably, they wielded some scary two-handed swords, which the Portuguese called montante which in the right hands was capable of cutting an un-armoured person (arguably the most common kind of foe the Portuguese faced in the east) in half, if the chronicles are to be trusted. But because they were nobles, they weren't really entitled to any standards when it came to arms or armour, so it varied; they also used shields, broad swords and halberds. Rather uniquely, these nobles were sometimes accompanied into battle by personal servants (slaves) who would carry their weapons for them.

Then there were the common troops. These were (usually) volunteers, for Portuguese forces rarely ever needed much more than a thousand or so troops in almost every campaign in the Indies. Malacca for instance was conquered with just 700 men and about 300 malabarese auxilliaries.

The "common troops" were usually provided with a helmet, breastplate and a pike. But they could (and did) complement this with their own armour. They also carried broadswords on them. One kind of sword became distinctive of the Portuguese, being called black sword, crab sword, but was more famously referred to by the common men-at-arms as... the "big balls". Their armour would also vary somewhat from man to man, depending of course on how much he had invested his own money into protecting his life. A fancier helmet here, additional vambraces there, that sort of thing.

Overall, all this provided an immense advantage over the masses of unarmoured Malayan troops, who wore at best chainmail, and even that seems to have been rare.

Common men-at-arms tended however to have very little training and were very undisciplined, for which Commander Afonso de Albuquerque maintained a corps of so called Ordinance troops trained in a strict military fashion by veterans from the Italian Wars and knew how to maneuvre in a formation and wield a pike and an arquebus indistinctively.

Finally there's one important aspect that limited the use of armour which was of course, the tropical weather conditions. It's extremely hard to fight under a torrid sun in a damp climate, much more so when you're clad in a heavy full body case of steel. Infact, on the first day of the attack the Portuguese stopped fighting the moment it became too hot in the middle of the day and fortified themselves on the city's bridge, on which they set up a canvas for shade.

Source:

Conquista de Malaca, 1511 by Vítor Luís Gaspar Rodrigues and João Paulo Oliveira e Costa.