Anyone have a suggestion? My space is always so full but I have no idea how to know what to keep, what to try and sell and what to just dump.
The game is kinda always like that, even with my fully expanded Exosuit, 48 slot ship, freighter and storage containers, it's always a bit of a struggle to keep your inventory with at least some free slots. It depends on what you're doing and what are your goals at the moment. The builders quests and the new story will require various resources so you can craft new technology and learn new blueprints.
As for the moment to moment, basic requirements,
check out this list. The names are now outdated for the rarer and more advanced resources, but the top 9 are the ones you will be using a lot as they usually fuel your ship, shields, life support systems and are used to craft some of the basic items like Warp Cells or for on-the-field tech like Signal Boosters used for finding points of interest.
To try to make this as short as possible (isotopes - red - fuel, power, oxides - yellow - shields, power and fuel, silicates - blue - mostly ingredients for basic and advanced crafting recipes):
Isotopes (red):
Carbon - Life support and multitool recharging. Extremely easy to find, basically every plant is Carbon, larger trees are a good quick resource.
Plutonium - Fuel for the landing gear and weapons. Red crystals, can find it everywhere, but due to the 25% takeoff cost, always needed.
Thamium9 - Charge multitool equipment and life support. Red flowers, common but in smaller quantities, kinda like Zinc. Often needed for some basic crafting recipes so it can sometimes be annoying if you don't have enough.
Oxides (yellow):
Iron - Fuel for the Pulse Engine (flying from one planet to another), extremely easy to find, every rock is basically Iron, also asteroids. Useful to have a bit stored, but you can get it anywhere in like 10 seconds.
Zinc - Recharging shields and tech. Yellow flowers, pretty common but in smaller quantities. Usually always useful to gather a few when you find them around.
Titanium - Like Zinc but rarer and more potent. Yellow crystals, much rarer than Zinc.
Silicates (blue):
Heridium - Most used and most common. Blueish columns of mineral deposits. This, as well as the other two Silicates are used in a whole bunch of crafting recipes. Relatively easy to come by though.
Platinum - Kinda like Zinc and Thamium9, pretty common but in smaller quantities. Blue flower, used in a bunch of recipes.
Chrysonite - Rarer and needs an Advanced Mining Laser. Blue crystals in smaller quantities, also used in a bunch of recipes.
All nine of these resources are also used for a lot of crafting recipes, but you'll mostly worry about getting enough of the larger mineral deposits, plants and rarer artifacts like Aqua Spheres, Vortex Cubes and the like.
Important to note that pretty much all of these can also be bought from station terminals or NPCs, so if you have a bit of cash (not that much), you can easily stock up on, for example, Zinc, Thamium9 and Heridium by trading with a bunch of NPC pilots while docked or with the station trading terminal.
Pugneum (from killing Sentinels), Mordite (from killing creatures) and stuff like Tropheum and Herox (from killing space ships) are always easy to come by. The first two are sometimes used in crafting, but very easy to come by. You can just sell the Tropheum and Herox.
The junk and goop you get from opening green boxes or cleaning up abandoned terminals doesn't seem to be used for anything, so you can just discard those.
The rest are mostly large mineral deposits like Nickel, Iridium, Copper, Aluminium etc, and plant resources like Marrow Bulb, Solanium, Frost Crystal, Fungal Mould and so on are used in all kinds of crafting recipes, but you'll just have to get used to them while looking at the recipes you have and what you want to craft next. I used to keep track of which materials were most used, but lots of stuff has changed over the last couple of patches so not that sure.
I'd say Marrow Bulb, Frost Crystals and Cactus Flesh are some of the most important plants.
There's probably more useful stuff that can be said about the resources, but it's really about what you need next, what tech you want to craft etc. so the more tech you install, the less you'll need some of the more exotic stuff.