Freighter ships are used to establish trade routes with other Civs (as Basilisk83 said - as long as you're not at war with them). Establishing trade with other Civs helps with their positive view of your Civ. You can only send them to Core worlds. I usually target capital worlds (esp. Minor Civ capital if close). I've always assumed the higher the output values of the world I pick will yield a better result, not really sure if that's true 
Supply ships are useful for jumpstarting projects in the beginning of the game when your production is low. They can be used to rush an important project when you don't have cash or control points. Yes, you can only send them to core worlds, including the one that built the supply ship. Later in the game you'll get a tech that allows you to build Industrial Goods which serve the same function, but can only be used on the planet where they are produced.
You can get more survey ships by surveying yellow anomalies. That's a random thing so you could get other types of ships instead. Right now yellow anomalies are not defended due to a bug the Devs are trying to squash, but eventually you'll need armed ships to defend you survey ship.
The other thing that you need to know is that while colonies can't be managed they do serve a very important use. They feed your core worlds with resources. This can make core worlds very strong when they have several colonies sending them resources, so try not to get "Core World Happy Feet"
