Use scan at the beginning (hit escape on keyboard or start on controller and select it from the menu up top). Look around for easy to access minerals.

Aim for at least 1 set of fuel and energy on your first landing, also a pair or Illumanite rocks, if you grapple all 8 pieces into a clump and attach them to the main thruster of your lander you should have no problem getting the whole thing to your ship.

Use the Illumanite to make titanium armor for yourself and your lander, this is a top priority, and will help you survive the weaker enemies.

Take the opportunity to blow up the first few spider ships that spawn, you can grapple the spiders to the floor or ceiling and reel them in to get them out of the way. 3-4 ships worth of salvage will get you everything you need for rank 2 Lander thrusters, this goes a long way towards improving your fuel efficiency.

Remember those spiders you stuck to the ceiling? Go back and snag 3-6 of them and grapple them into a clump, then go refine them. It's a little tricky, but the best way is to take a few on a long tether, land them on the top right of your mothership and land your lander on the left side. Sometimes they will follow the walls towards you and walk right into the reactor! If not you may have to go down there and give them some help by grappling them up into it.

By now you should have almost everything you need for most T1 upgrades, focus on keeping your fuel and energy up, snagging any hyper fuel you can find.

You can also grapple wasps, and give them a similar treatment to the spiders, although as you try to fly off with them attached to your ship they will fight your momentum, so this is easier to do with small groups and upgraded Lander thrusters.

Proceed to warpgate!

That's about it, try these things out and let me know if they help, as a final note, less is more when it comes to your Lander's lateral thrusters, and if you find yourself spinning in the wrong direction, cut your main thruster until you're poainted in the right direction. This will help you to not end up with bad momentum!

Cheers!