Hi, I'm not sure whether or not you would be the right person to ask.
Back when Christianity started, there were many different sects. How did the Orthodox Church which later became modern day Christianity "beat out" all those sects?
I think you're maybe summarizing things a little too neatly. During the very early days of Christianity, there weren't actually "sects." There was "the church" and there were a variety of offshoots that were considered heretic, i.e., not Christian at all.
Also, the Orthodox Church did not become "modern Christianity." What would later become the Orthodox Church was formed in 1054, in "the great schism," which also formed what would eventually be known as the Catholic Church. Then, of course, there was the Protestant Reformation, which further split things, and so on and so forth.
Anyway, as for how the "official" form of Christianity "beat" those other offshoots way back then is fairly simple: it had more adherents due to being spread more widely for whatever reason. Rather the same way that Christianity would later "beat" a number of pagan religions around the world. The church had money and was able to send emissaries far and wide. (I suppose threatening to kill anyone who didn't convert might have helped, too.)
I'm sure a little Googling will turn up sites that talk about the earliest denominations, if you're interested. It's rather entertaining to learn about the petty little things that made group A differ from group B.