If you started with Conventional Start, it means you have to research all the technologies it will take to get you there. For a first-timer, you'd be better off restarting with a "normal" start, which starts you with some technology already researched.
Keep in mind once you have an engine technology (say Ion Engine), you then need to design and research an actual engine: whether its for a military ship or a civilian ship, whether it has thermal shielding or not, whether you want it to be more explosive prone (and have more power) or less so, and so on.
For a geosurvey ship, you need geological survey tech explored (plus all the other things it takes to build a ship: fuel tank, bridge, engines, crew quarters, etc etc etc). You'll know you have a working survey ship if in the F12 Fleet window you see a number greater than zero in the Geo Survey point field (just under the Race/Fleet/Task Group dropdowns). After that it takes time.