This great game was released for the PC back in 1996. In it you select one of several pre-made races or create your own with various bonuses and weaknesses. But before that you select custom aspects of the galaxy.
There are three routes to victory: conquer all opponents; be elected as the supreme leader of the galaxy; or make a successful assault against the Antaran home world. To be elected, a player needs two-thirds of the total votes, and each empire's votes are based on the population under its control.
To that end you will be researching new technologies, making alliances and trade/research agreements. There is also colonizing new planets/systems, upgrading your infrastructure and building up your forces.
From time to time leaders will approach you with special abilities than you can assign to manage star systems under your control or to one of your fleets to improve combat performance. There are also random events than can occur and can be good or bad, these events are portrayed in a galactic news alert.
It is arguably the most popular in the series and was published by Microprose who also published X-Com. Overall it is an excellent game that has a very high replay value. You can also buy it for about $6 over at GOG. Master of Orion 1+2 at GOG