Science
Each of the 20 locations has 5 different science objectives that can each be completed for rewards exactly once. You'll get science points as soon as you complete an objective. Each of these objectives makes up 1% of game completion. You can click the research tab on any planet with a lab to see your current completion.
Fly-by (1 point) - Occurs the first time you are caught in the gravity of an object. You'll know this happens because your trajectory will change to be relative to that object.
Orbit (2 points) - Occurs when you complete one full orbit without firing your rocket. Note: it's not enough to be "in orbit" you have to go all the way around.
Land (2 points) - Occurs when you land safely on a new location.
Return (2 points) - Occurs when you travel to a new location and then return to Earth or a location with a colony. This sequence is broken by resetting or crashing. You must safely travel to and from a location to get the reward. This reward also unlocks the ability to build a colony on the new location, so it's critical for expanding your reach into the outer solar system.
Lab (3 points) - Occurs when you build a lab at a location. In order to build a lab you must already have a colony.
Ship Upgrades
Navigation - Increases the number orbital transfers that are predicted in the UI. This is very useful for planning gravitational slingshot or braking maneuvers and making sure you won't crash when you arrive somewhere. Recommended as first purchase.
Fuel - Increases the maximum regular fuel you start with. A solid second purchase.
Thrust - Increases the rate of acceleration when firing your rocket. This doesn't increase fuel efficiency. It simply allows you to make maneuvers faster. Nice but never required.
Land - Increases the maximum speed that is considered safe for landing. Convenient, but really only critical for landing on Jupiter.
Launch - Increases the amount of bonus launch fuel you get when launching from planets with launchpads. Can save a lot of regular fuel, but not always useful. Critical for getting to Venus (spoilers).
Buildings
Station / Fuel - The first thing you have to buy. Refuels your ship on landing. Allows other purchases.
Colony - Requires return science completion to build. Counts for completing other return science. Allows picking up a mission on this planet. Allows building a lab.
Lab - Allows purchasing ship upgrades and viewing the science completion window. Rewards 3 science points when built.
Launchpad - Gives bonus launch fuel bar when launching from this location. Unlocks brakes.
Brakes - Increases the maximum speed that is considered safe for landing at this location.
Satellite - Requires all other buildings before it can be built. Refuels your ship in low orbit.