The GTVA didn't meet any species before the Shivans. So there was not much conquering to be done. Well, aside from meeting eachother of course, which as we all know ended up with both sides trying to conquer the other until the real bad guys showed up 
Na, they weren't trying to conquer each other. It was more like,
Terran - "I don't like your shoes, I'm gonna kill you now."
Vasudan - "Well, I don't like your gloves, so we're gonna demolish your existance!"
The ancients were more like,
Alien - "Hello, we come in peace."
Ancient - "Omg! Its a bunch of inferior people! Lets enslave and/or destroy their civilization!"