Rome was originally a town built amidst seven hills surrounded by swamps in central Italy. The Romans were just one group of “Latins,” central Italians who spoke closely-related dialects of the Latin language. Rome itself had a few key geographical advantages. Its hills were easily defensible, making it difficult for invaders to carry out a successful attack. It was at the intersection of trade routes, thanks in part to its proximity to a natural ford (a shallow part of a river that can be crossed on foot) in the Tiber River, leading to a prosperous commercial and mercantile sector that provided the wealth for early expansion. It also lay on the route between the Greek colonies of southern Italy and various Italian cultures in the central and northern part of the peninsula.
The legend that the Romans themselves invented about their own origins had to do with two brothers: Romulus and Remus. In the legend of Romulus and Remus, two boys were born to a Latin king, but then kidnapped and thrown into the Tiber River by the king’s jealous brother. They were discovered by a female wolf and suckled by her, eventually growing up and exacting their revenge on their treacherous uncle. They then fought each other, with Romulus killing Remus and founding the city of Rome. According to the story, the city of Rome was founded on April 21, 753 BCE. This legend is just that: a legend. Its importance is that it speaks to how the Romans wanted to see themselves, as the descendants of a great man who seized his birthright through force and power, accepting no equals. In a sense, the Romans were proud to believe that their ancient heritage involved being literally raised by wolves.
The Romans were a warrior people from very early on, feuding and fighting with their neighbors and with raiders from the north. They were allied with and, for a time, ruled by a neighboring people called the Etruscans who lived to the northwest of Rome. The Etruscans were active trading partners with the Greek poleis of the south, and Rome became a key link along the Etruscan - Greek trade route. The Etruscans ruled a loose empire of allied city-states that carried on a brisk trade with the Greeks, trading native Italian iron for various luxury goods. This mixing of cultures, Etruscan, Greek, and Latin, included shared mythologies and stories. The Greek gods and myths were shared by the Romans, with only the names of the gods being changed (e.g. Zeus became Jupiter, Aphrodite became Venus, Hades became Pluto, etc.). In this way, the Romans became part of the larger Mediterranean world of which the Greeks were such a significant part.
According to Roman legends, the Etruscans ruled the Romans from some time in the eighth century BCE until 509 BCE. During that time, the Etruscans organized them to fight along Greek lines as a phalanx. From the phalanx, the Romans would eventually create new forms of military organization and tactics that would overwhelm the Greeks themselves (albeit hundreds of years later). There is no actual evidence that the Etruscans ruled Rome, but as with the legend of Romulus and Remus, the story of early Etruscan rule inspired the Romans to think of themselves in certain ways - most obviously in utterly rejecting foreign rule of any kind and even of foreign cultural influence; Romans were fiercely proud (to the point of belligerence) of their heritage and identity.
By 600 BCE the Romans had drained the swamp in the middle of their territory and built the first of their large public buildings. As noted, they were a monarchy at the time, ruled over by Etruscan kings, but with powerful Romans serving as advisers in an elected senate. Native-born men rich enough to afford weapons were allowed to vote, while native-born men who were poor were considered full Romans but had no vote. In 509 BCE (according to their own legends), the Romans overthrew the last Etruscan king and established a full Republican form of government, with elected senators making all of the important political decisions. Roman antipathy to kings was so great that no Roman leader would ever call himself Rex - king - even after the Republic was eventually overthrown centuries later.