Once the snowball effect starts, start buying only early and improvements in new colonies, to save for buying Technologies. Buying out as many improvements as possible will quickly snowball their industrial machine, allowing the mass-creation of ships or a push towards a Wonder Victory. Influence Luxuries, especially, for System Development Projects are also heavily recommended if they can be seized. Any improvements or other bonuses that reduce the buyout cost will also reduce the buyout cost, so prioritize (-10% buyout) for rank 1. While The United Empire can thrive only with buyout, researching the standard buyout is still recommended. Like the Sophons, the United Empire is another faction good for beginners, mainly because this empire tends to be versatile.
Their ability to buyout improvements with, their feedback from system production, and the bonus of feedback make them a powerhouse for system improvements and ship production. The United Empire excels at Wonder Victory, but their strengths apply well to any victory type.