Are you still in Sol? You may want to wait until you explore a few more systems and maybe find a half-decent world to colonize. Anything under Colony Cost of 2.0 is decent enough as long as you drop enough infrastructure.
But, to test and get used to the process you could build a Freighter with 25000 Cargo, then have Earth build a pile of Infrastructure. Give the Freighter repeating orders to move infrastructure to Mars. Once it has done a few runs you then have the Colony ship do some Colonist runs. Just make sure not to place more colonists than the infrastructure can handle. You can also try to terraform Mars, but at early stage that will take a long-long time.
In time a Civilian Shipping Line will form and should build its own Freighters and Colony ships, in effect they take over the colonization - up to a point.
Of course, you should have an economically viable reason for starting a colony, such as a way station along a long warp chain, or good mineral deposits or as a fleet base. That means that over time you need a plan to move facilities there, which either means your own expanded Freighter fleet, or setting up civilian contracts to move your facilities for you.
As for the mineral deposits you have atm, make sure you have a surplus of Mass Drivers on the Earth at all times, then move ONE to an asteroid along with a repeat order of automated mines, move about 50 to start and see what kind of mineral flow you are getting from it. t is crucial you leave some Mass Drivers on Earth, Aurora will NOT tell you if you move the last one. If there are no Mass Drivers on Earth to catch the mineral packet then you will end up ruining the planet
You can set the Mass Driver destination on the minerals screen of the Economy window (F2?)