If we're sticking to the Roman Kingdom, they didn't really conquer anyone. The Roman Kingdom was extremely small, and seen by contemporaries as essentially just another city-state. They fought as hoplites in a phalanx, and their wars were equally small-scale - think cattle rustling and responding to cattle rustling. Each side would form up, fight a little war, the winner would get the spoils, and a peace would be formed. According to Livy, the Romans basically won all of their battles, but this area of Roman history is heavily shrouded in myth and legend. There's very little known about this time period, sadly, but the most major military development (probably) was the introduction/solidification of the social strata along class (wealth) lines by the sixth king, Servius Tullius.

Class	Property in Asses (bronze coin)	Expected Equipment	Junior Centuries	Senior Centuries	Total centuries
I	100,000	Helmet, round shield, greaves, cuirass, spear, sword	40	40	80
II	75,000	Helmet, oblong shield, greaves, spear, sword	10	10	20
III	50,000	Helmet, oblong shield, spear, sword	10	10	20
IV	25,000	Light shield, spear, javelin	10	10	20
V	11,000	Sling, stones, possibly javelin	15	15	30

There were also “supernumerary” centuries, which were outside of the above class system:

• 18 of cavalry: These guys were the wealthiest of the wealthy, and were known as the equites. The only downside to having your rich guys in the cavalry? They’re really horrible at doing things which they consider to be menial. Like scouting. This becomes really significant when Hannibal comes along.
• 2 of engineers: Rome was known for her engineers and the marvels which they produced. The distinction of these engineers is a mark of that, as they were allowed to vote independently of their wealth class.
• 2 of musicians: They were the guys who kept the army going. While they weren’t quite as honoured as the engineers, the musicians were also slotted into their own classes.
• 1 of the capite censi - the ‘head count.’ So poor they weren’t even expected to serve in the military, and were just a number. 500,000 men in one century? Basically, that’s these guys.

Soldiers provided own equipment, especially in the first 500 years of Roman history. Things begin to get murky in the Punic Wars due to massive losses of manpower, but having weapons and being able to provide them in service to the state was a mark of pride for many Roman families. It was their way of showing how they not only lived in the City, but truly were willing to fight to defend their homes.

One final note: The centuries didn't have a specified number of people in each. The lower centuries always had a ton more people in them than the "higher" ones.