Once you’ve ‘unlocked’ as others have said, X onto a neighboring star to see information about it. Once you find the Economy and Conflict Scanners, the current state of the system will be displayed giving you a more informed choice. You can always see how many planets orbit the star, any moons as well as if it is in your jump range, (make sure your warp drive is fueled first) but if you can’t reach a star in one jump, you can set a Custom Waypoint and flicking through along the top with the shoulder buttons will cycle your active waypoints, (choose to follow the path of the Atlas/Anomaly etc)
I would definitely advise getting an Economy scanner as soon as possible, (purchased with nanites in space-stations) as visiting high wealth systems have the best chance of spawning top level ships etc.
If you’re after a Lush, Earth-like world, (leafy or watery), aim to visit Yellow stars as the chance is higher with this colour.