As you are new to Elite

angerous, you need to complete the basic tutorial. That will teach you everything you need to get started. After that, don't worry about trying to get money. Just focus on trying to apply the tutorial to the full game. Once you are comfortable and have a basic mastery over the simple things, try to learn things that might be just out of reach. Do some missions, find a Resource Extraction Site and make some kills, try trading without using the missions, be a pirate. Don't worry if you are still in a Sidewinder two weeks from now. If you crash a few times, laugh it off. I recently died because I caused my own death by trying a bombing run too close to the ground after slamming into the surface of a planet. Lesson: don't slam into the ground and try a low-level bombing run shortly afterword. Mines explode when they get too close to a target!
When it comes to climbing into a new ship. Save up your credits. There are few things worse than buying that ship you've been drooling over only to realize you can't get to another star system because the new ship just can't quite reach or having not having enough money to cover the re-buy should you be destroyed.
If you have Horizons, you'll be able to get close to a planet (provided your graphics card can handle it). My father had to get a new graphics card because his old one was unable to handle the generation of the surface map. If you have a 2 Gigabyte graphics card (plus E: D Horizons) then you're fine. Just keep it slow as you get close, drop to 200Mm/s or slower, and allow your ship to slow further to 2.5 Km/s. And stay out of the red when the side bars show up. You'll drop if your ship's approach angle touches it.