In the ability selection menu, there's also a button to increase the capital ship's level at the cost of about 1500 credits (depending on what level it is, and discounted based on how much experience is required before it levels up).
To get artifacts, you click on the planet and select the planet upgrades menu. One of the upgrades available is called "explore planet". If the planet has an artifact on it, you'll find it by purchasing this upgrade. This is a gamble, however, as not all planets have artifacts or other bonuses.
