I would say possible spoilers, but really, there's barely anything that can be spoiled about the game as far as I know. And what there is, I won't be spoiling.
Press melee, then immediately use your jetpack. Gives you a huge speed boost while jet-packing.
Save your atlas stones if you want to finish the atlas path! You need 10 of them to finish it, and you get exactly 10 from said path. Otherwise you'll have to search for traders that sell them and they will cost 2 mil or more.
On that note, finishing the atlas path is helpful if you want to reach the center. At the end, black holes will be marked on the galactic map for you without asking Nada. You only jump about 400ly from warp jumps, but 1500ly on average with black holes.
If you're looking for a new ship, don't wait in a hangar/trade post for ages. The same ships will spawn over and over again. After you've seen like 6~8 different ships, fly away for a few seconds and come back. New ships will spawn. Same goes for what you can buy from said ships.
For best money making: Find a planet with sac venom on it, and search for trading posts/markets. Install the shotgun addon for your multitool (forgot the name), and shoot the sacs with the boltcaster. It destroys them in 1 shot, because of that sentinels don't aggro, and you can snipe them from far away.
Don't farm for the atlas pass v2/3. What you find behind those doors is useless. It's nice if you happen to stumble upon the blueprint, but that's about it.
Install all warp drive upgrades. Different coloured stars need different warp drive upgrades. And more rare resources spawn on 'higher' colours. The order is Yellow (starter star) -> Red -> Green -> Blue.
Don't let your multitool overheat to where it cools down on it's own. Stop shooting for half a second so the animation stops, then continue. It resets the entire heat bar.
Really, don't hurry to the center. There is no need. (Not 'that's not the goal of the game'. I really mean 'there is no need'.)
If you need to find an anomaly (space station with nada on it), explore planets a little bit. Scan some animals, clear some buildings, etc. THEN warp to the next star. The anomaly only has a chance to spawn (or at least a higher chance) if you explore stuff a bit in star systems.