This is a quick-and-dirty build tutorial for a ship build I posted to Reddit the other day. Please let me know if you have any suggestions or feedback about the build!
In terms of building this in pieces before you have all the parts, I usually fly around in another 'completed' ship while I put whichever ship I'm currently building together. I usually go to New Homestead first to get all the landing gear I need, as well as the cockpit in this case. I would then recommend going to one of the Stroud-Eklund vendors or building most of the ship on the larger ship landing pad that you can build in one of your settlements. I would recommend going to the Stroud-Eklund staryard in the Narion system, as you can then hop to the Valo system to get the HopeTech parts. Then I would go to the Deimos shipyard last. In place of bigger habs or specific habs from a different company, I usually slap in whichever 2x1 habs I have access to in order to fill the same space. As you build this, you can slap in whichever habs or structural parts you need in order to satisfy the flight check errors from the shipbuilder. It doesn't matter how the ship looks during these building phases, as long as the ship builder will let you save and exit. The locations of specialty ship part vendors are detailed below.
The Nova Galactic 'specialty' parts (landing gear, cockpit, larger habs, weapon mount, and cowlings) you can get from New Homestead, on moon of Titan which orbits Saturn, in the Sol System. The ship technician outside the landing pad here is your guy.
The Stroud-Eklund 'specialty' parts (caps, cowlings, and bigger habs) can be found either at Neon or at their staryard. Their staryard is in the Narion system, orbiting the Dalvik moon of the Deepala gas giant. Note that the Narion system shares a 'node' in the starmap with the Valo system. Havershaw is your NPC vendor here (if you don't see him he's either at the first desk you see, directly ahead in the showroom desk around to the left, or hiding in the potted plant behind the chair that's facing his desk but in front of it). Neon is in the Volii system on the planet Volii Alpha. For just cowlings and non 'specialty' parts, the ship technician in the ship services building next to the landing pad here can help you, and there is a Stroud-Eklund storefront in the Neon Core area. Walk out of the elevator from the ship landing pad and take a right, and the shop will be just past Sieghart's Outfitters on the left side of the strip. Use the computers in the wall here to modify your ships.
The HopeTech 'specialty' parts (the radiator and bigger habs) can be found at HopeTown in the Valo system on the planet Polvo. Note that Valo shares a 'node' in the starmap with the Narion system. The ship technician here sells all the structural parts and the 2x1 habs you'd need, and if you keep going straight ahead into the lobby of the huge HopeTech building you see as you exit your ship, there is a vendor in the lobby on the right side behind a wraparound desk.
The Deimos 'specialty' parts (larger habs, landing bay, structural parts) can be found at the Deimos staryard. This is located in the Sol system orbiting the Deimos moon of planet Mars. As you walk in, stay to the right and continue down the stairs to find Nikau Henderson in a UC navy dress uniform.
In order to build a new ship you'll need to start from an existing ship. You can either capture a ship using EM weapons and/or the ship targeting perk or buy the cheapest ship you can find from a ship technician. To register an acquired ship, go into your inventory, go to the ship management window, and there will be a button on the bottom that says register, which is G by default on keyboard. While you can also register ships with any ship technician, it's cheaper to do this directly from your inventory. If you're going to use a captured ship, I would recommend that after clearing it you hop into the captain's chair, set this new ship as your home ship by going into your ship inventory and pressing H by default on keyboard, then un-docking and re-docking with the ship you flew in with. You can then get back on the ship you flew in with, set that as your home ship, and go about your business.