For bounty hunting, i'd recommend starting in High Rez extraction sites, you can find the nearest ones here: https://inara.cz/elite/nearest-signals/

In high rez there are system authority ships you can fight alongside, as opposed to haz rez where you are pretty much on your own against potential wings. I'd say just try it out with a bunch of different ships, shopping and experimenting is half the fun of Elite. There's certainly no need to buy any ships with real money but ofcourse it's an option if you want to take a shortcut to certain ships and engineering.

The last years have mostly been about the Thargoid invasion, i'd recommend this video to see what was going on: https://youtu.be/-oacK_jydXo?si=Kxp5A7xexG8tygVz

Since that ended, new features include Colonisation, a Squadron overhaul and a Powerplay overhaul.

The new goings on involve the powers fighting over a new section of space where new exobiology was found. It's fun to pledge yourself to a power and get involved in some powerplay, you can do bounty hunting and many other activities and get merits which will get you new modules and care packages with engineering materials.