Wide-angle zoom
$$$Most landscape compositions live at 16–35mm. A zoom lets you work a ridge without swapping glass in the wind, and a good one is sharp by f/8 — which is where you will actually shoot.
What to look for: About 16–35mm on full frame (10–24mm APS-C), reasonably sharp stopped down, weather sealing is a bonus.
Skip it if: you already have a kit zoom that starts at 16–18mm and you are happy at f/8. Spend on a polarizer first.