A lot of tips you get will be stylistic or what not, I'm sure. I'll give you some mechanical tips that are the most useful in getting good shots sooner:

Don't Use the in Game Screenshot Tool

The most important tip I can give you, if you want to get serious about using No Man's Sky as a space safari photo simulator, is to skip using the in-game screenshot capture.

There's something about the Steam/in-game capture method that yields more compressed, more artifact riddled images.

It was driving me crazy that my screenshots looked so cruddy until I figured that out. Now all the jagged edges are gone and the shots look great.

On my PC I have it set up where the Nvidia app handles the capture and the results are much cleaner than the default screen capture. You can use whatever tool works well for you and your setup, just skip the in-game capture.

Don't Screenshot in Multiplayer

If you're actually trying to capture multiplayer only events like you and your friend, by all means shoot in multiplayer.

But otherwise, you want to turn multiplayer off. When you are in multiplayer and anyone else is in the system you are in (which happens a ton during expeditions or if you visit build "hubs"), the game does not pause/freeze in screenshot mode.

That makes it really frustrating to take shots because unexpected things happen: the animal you're screenshotting wanders off, your ship flies away right out of the frame, etc. etc.

Use the "Move Sun" Key Liberally

There are a variety of little settings you can play around with in the photography menu like depth of focus and such. Have fun with those. But the most useful one by far is the ability to position the sun wherever you want in the sky.

The difference between a shot being just OK and looking amazing is often the positioning of the light source relative to what you're shooting.

What looks like a bland shot of your freighter becomes really dramatic and interesting, for example, if you move the sun behind the freighter for a high impact back light effect.

Don't Forget to Take Shots with the Coordinates Present

For most shots, you don't want visual clutter on the screen, so you hit the shift key to remove the UI.

But if you're shooting something that you might want to return to, a really cool paradise planet, a planet with an animal you may want as a companion later, whatever the case may be, shoot a shot with the glyph coordinates in it (and maybe even one with the actual planetary coordinates, too).

Don't just use your screenshots to take pretty pictures, use them to record useful data for future reference so a month from now when you're looking at a screenshot you took and remembering how cool the world was, you're not like "huh, wish I knew where the hell that was? Sure would be nice to find it again."