Edit: i started Typing this out before you replied ^^^^
Read this to get started, you can rent better ships with money you earn if you want to do more specialised missions.
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If you're starting out and don't have specialized ships in your fleet there are two things i would avoid.
Cargo trading: Need a ship with reasonable amount of Cargo holding capacity, Cutlass Black minimum, buy cargo goods and any trade terminal and move the cargo to another location to sell for a profit, you need to learn trade routes, where to buy what cheap to sell elsewhere at a profit, there are spreadsheets for this around the internet, careful tho some of them are out of date.
Bounty Hunting (Live Player and NPC) / NPC escorts / NPC Pirate clear-outs: NPC are easy but if you don't have a ship with some fighting capabilities you will struggle or find it impossible to hurt some ships, you're not going to take on a Valkery with an Aurora MR.
Dedicated fighters Anvil Arrow minimum, great little ship that actually. An Aegis Avenger also has reasonable fighting capabilities tho the Arrow is more dedicated to that role and capable of taking on heavier ships.
Other than that you can play postman by moving boxes around and get paid for it, sounds idiotic but actually doing it you're travelling around the verse, its a good way to see locations and its something that i like to sometimes do because its low stress, its relaxing.
First person mining: get yourself the mining tool and a backpack, go searching for minerals and mine them, sell the raw materials at trading points.
Surface side FPS missions, get some armour and some guns, go to Hurston and play the unwanted residence missions.
There's a PI mission where you go to a blown up station to figure out what happened.
There's more, just spend sometime in there you'll find things to do, interact with players and Multicrew, that's often fun.
The best stater Ship, a good all-rounder. Avenger Titan
https://robertsspaceindustries.com/pledge/ships/aegis-avenger/Avenger-Titan
Anvil Arrow
https://robertsspaceindustries.com/pledge/ships/anvil-arrow/Arrow
Cutlass Black
https://robertsspaceindustries.com/pledge/ships/drake-cutlass/Cutlass-Black
You will need a game package, just get this and upgrade the MR to the Avenger or one of the others. it will cost you the difference in ship value
https://robertsspaceindustries.com/pledge/Packages/Aurora-MR-Starter-Pack