This is the current list of Human Ships as of the 0.9.7 update.
This page may contain Spoilers.
Ships can be purchased through the Shipyard which can be found on many planets through out the game. However, not all planets have Shipyards, and Shipyards do not always sell the same ships.
The Starting Ships are quite good in many ways, and there may be downsides to upgrading to other ships that players should be aware of before purchasing.
Many Transports, and all Fighters and Interceptors, require only the default player Crew. But all other non-Starting Ships of other classes require a paid crew, at 100 credits per day each crew member. This can be a drain on the resources of an Explorer-type player, who wants to wander the fringes of the galaxy where opportunities to profit are fewer in number, if not in value.
Qualities that make the Star Barge an excellent starting ship make its potential upgrades look less like an improvement. There is no other Light Freighter with the acceleration of the Star Barge; the Clipper is almost the same, and is 24% faster, but the Clipper has only 20 more cargo space, costs 1 million more credits and can only be purchased in the southwest corner of the galaxy. The rest of the Light Freighters, of course, have more cargo space, but they are all significantly slower in comparison.
The categories of ships are something of a rough guide; a large proportion of ships, if not the majority, are hybrids. This is especially true when the customization capabilities of outfits (Human Outfits) are considered.