Just landed on a planet, what should I be looking for in order to start building my base?
At the very beginning, without being able to go too far, it's really important to find Compound so you can craft Tethers and go seeking for an interesting cave where you can get a lot of Resources. After you can move far away from home and have a "tethers' net", you should focus on finding energy and resin, being this one the most important as it's the material used for building modules and links, the basic structures of the game.
Whenever you get to this point, where you already have some usefull modules and energy generators such as solar panels or turbines, I'd suggest going for copper used for the Printer but this is just a personal preference.
1 and 2 you need LOTS of.
1 - Resin. Its required for base modules. Without it you can't expand your base which means you can't make anything, can't research anything, and can't generate much energy.
2 - Compound. Its used in construction of the majority of the things you need early on such as tethers and medium storage panels. And beacons.
Nice to haves...