How i made my first few hundred thousand or so.
1) Take courier missions or light delivery missions. Do not bother with go-for missions, because it can be tricky and requires initial investment from you. Don't worry about the timer. Most deliveries can be completed in around 5-10 mins. They also tend to have long deadlines, so if you need to AFK for a while its not a problem - just check the timer for the mission before accepting it.
2) Every time you jump into a new system for which you do not have data, do a scan. You then sell that data whenever you are > 20LY from the system you scanned. Its not much, but is effortless. Alternately, you can sell your basic scanner and fit a small cargo bay in its place allowing a little extra space for delivery missions.
Do that for a few hours, you should have enough money for an Eagle or a Hauler. Go for the Hauler if you would like to do trading (in which case, i'd recommend you read up on rare item trading) or exploring. Go for the Eagle if you would like to try your hand at bounty hunting, although have a care, the Eagle is made of paper, so choose your targets wisely until you get some upgrades and skill. Go hang out a nav beacon and look for low ranked Sidewinders and Haulers that are wanted.
Fly safe commander.
PS: Oh, never ever fly without enough money to cover your insurance. Number 1 cause of ragequit.