No Man's Sky

It's easiest to follow the missions, at least at first. There's a base-based mission set that gradually has you craft and fill all the different base components as well as do some farming. There's two branches of exploration style missions.

"Number of slots" is pretty much king in terms of your multi-tool and your ship. Inventory space is at a premium and is what you'll use the most so consider that before trading up to a ship that has more plusses but less inventory. Last time I played, ship combat ranged from bad to awful, I just avoided it when I could so I didn't care about weaponry. Maybe it's better? You'll want to upgrade Fuel efficiency since warp fuel is the most annoying thing to get.

Keep an eye on market prices! By mid game, it will be faster to just buy stuff that's annoying or has multiple steps to craft (looking at you, warp fuel).

You get a free freighter ship after a bit. It costs warp fuel to travel inside it, but it can be 'summoned' to you for free so it's most economical to warp in your ship and then summon it. It's an OK mobile base, but it's just as easy to portal around. Be warned, if you upgrade your freighter you lose everything inside it as the configuration resets! If you want to game the system to get a good one,
You get the freighter after 3hrs of continuous play and 5 system jumps. If you save with a portable save point on a planet in each system prior to the last jump, you can reload and and try again until you get a good one. The richer the system the better chance for a S class freigther

You can have an unlimited number of bases and you quickly get magic portals that can link them. Since you can summon your ship to you at any time, this is effectively fast travel to different planets/systems with valuable resources. Where you are in the galaxy doesn't really matter, except to remember the 'furthest' you've been and continue there, otherwise you'll have to rediscover where to go. I recommend you pick a neat looking planet for your "main" base and keep satellite bases for resources you need to gather. If you dig multiplayer interaction and want to check out / show off bases, check out building a base on one of the Galactic Hub planets.

When you are landing on a planet, first thing to do is hop out and do a scan. This "spawns" points of interests nearby; if you are looking for something specific (blueprints) you can search for that specific thing, then once you finish the base, you can scan again and chain them together. Don't forget to pick your scanner back up!

If you want the 24-slot multtool, an exotic ship, or good freighter of A or S type, you can check out the wiki but you basically go to a system and use the same method as the spoiler text until you're happy. It's fastest to check reddit, get the coords to your chosen system and use them to travel there (find a stargate portal) and get it. If you find something to share with the world, use this to get the coords: https://nmsportals.github.io/ (mostly unnecessary now as screenshots embed portal coords with the beyond update)