A new ship costs 10,000 credits. When you finish a run with enough credits, you will be prompted to buy one of the other ships - the Scout or the Gunship. Before buying a new ship, I would recommend spending your first few runs worth of credits at least on the Credit Loot Bonus: all other perks are purchased with credits, so it's the best early investment. This is a pilot perk so it works across your ships. You can invest in some other ship perks too to make your early runs easier (Energy Core especially) but they won't help you in your new ship. You'll eventually need to buy both, as there are achievements for doing 15 runs in each of the additional ships.