No Man's Sky

• You will not have immediate access to all the stuff you add to the shared expedition inventory. So don't bother adding metal plates, a hermetic seal, dihydrogen jelly, etc. because you will have to work through all the usual beginning steps to fix your ship and get off world.
• You will be able to return to the Anomaly about halfway through Phase 1, right after your first warp to a new system.
• BUT like with all the other expeditions, there are a handful of later phase milestones you can knock off quickly right from the initial system (or even the initial planet).
• For the base building milestone early in Phase 1, DO stash stuff in your ship so you have 9 empty slots in your exosuit. The base computer will give you everything you need to start your base and check this milestone off, but only if you have enough space for it to give you the parts.
• Scan everything, you will pick up the flora and fauna scan rewards quickly; dig up mineral deposits, ancient artifacts, buried caches, those all count for the lost treasure milestone (salvageable scrap does not seem to count here?). Blast asteroids. Learn words. The usual. Oh, and grind grind grind for nanites constantly, because:
• once you reach the anomaly, you will need a bunch of nanites. From the Expedition desk, you can clone whatever your then-current multitool and ship were before you started the expedition, but you'll need 2,200 for the MT and 2,800 for the ship.
• Similarly, if you want to grab previous expedition rewards, say, the Golden Vector, with the thought of maybe packaging up its modules to sell for more nanites (for example), well, it will cost you 1,400 nanites to pick up the ship :/ I also don't know what happens to the GV in your main save inventory if you acquire and then scrap a GV in the expedition, and I'm not sure I want to risk it. I will try to sell the mods for nanites though...once I have enough to acquire it!
• oooh! you will pick up various modules as you progress through the milestones, like usual, and if you are like me, you will not immediately apply them, since you will pick up a better ship/MT later in the expedition, more than likely. Well! If you started from your main save, you know you will get your main save ship and MT, so you can scrap all those scanner modules and such right away. That goes to the top of the to do list, I tell you hwat...

Happy exploring, travelers!