You can do Atlas and Artemis in whatever order, but Artemis is more rewarding in the short term, and has fewer requirements.
Broadly speaking, here are the rewards of each:
Artemis:
- Lots of blueprints, one crashed ship, a few other goodies. Most of these blueprints can also be purchased aboard the Space Anomaly, but Artemis will give them to you for free, and that will save you a lot of nanites and technology modules.
- Many of these spin off into brief side quests rather than becoming direct quest rewards.
- Towards the end of the quest line, the following:
A one-time shortcut to another galaxy. For most players, this will be their choice of Calypso (Harsh), Eissentam (Lush), Hilbert Dimension (Norm), or Budullangr (Empty), but other destinations are possible if you've already left Euclid. You select the type of galaxy you want, and the game will bring you to the next galaxy of that type. If unsure which to pick: Hilbert Dimension (galaxy #2) is reachable from the center of Euclid (galaxy #1 and the starting galaxy) through regular gameplay, Calypso (galaxy #3) is reachable from the center of Hilbert Dimension, and so on, wrapping around at Iousongola (galaxy #255 and the final galaxy). Budullangr is galaxy #7, and Eissentam is galaxy #10. Any planetary biome can generate in any galaxy, but around yellow stars, the galaxy type influences which planet biomes are most probable. Since Calypso and Hilbert Dimension are relatively easy to reach from Euclid anyway, you might prefer to select one of the other two instead. You can always return to Euclid through the teleporter system.
Atlas:
No intermediate rewards (that are useful for anything other than the next part of the quest). Upon completion of the full line:
Black holes are visible on the galaxy map. Blueprint for an exosuit upgrade which increases core health (not shields). Blueprints for a series of items that can be used, together with a blueprint from the end of Artemis, for another exosuit upgrade with the same effect plus access to a few bits of lore. These upgrades synergize if placed next to each other, giving you a total of +3 health.
Atlas also requires you to complete milestones to progressively unlock it, whereas Artemis is all unlocked from the beginning of the game. Milestones are completed automatically through regular gameplay, so there's no need to grind for them unless you're trying to speedrun the quest line.
The Space Anomaly:
Quicksilver and nanites, each time you talk to Nada. You can talk to Nada after most quests in either of the other two storylines. While you're there, you may as well also get free nanites from Helios and Ares.