Must-Have Brushes

Both Morphe & Sigma have similar brushes and qualities. If you find the same type of brush on Morphe for cheaper, it will be just as good!

Morphe Brushes

+ M435 Large Contour Blush- bronzer, blush
+ M556 Detail Contour Fluff - bronzer, blush or face blending
+ M438 Pointed Contour - highlight, more precise bronzed contour
M514 Detail Round Blender - eye crease
+ MB23 Round Blender - eye crease to brow blending
+ G27 Pencil Crease - lower lash line blending

Sigma Brushes

E15 Flat Definer - lower lash line definition
+ F80 Flat Top Kabuki - foundation
+ E30 Pencil  - the best lower lash blending brush I've found

NARS Ita Kabuki Brush - precise contour

beautyblender - foundation, concealer

Other Brush Brands

Since everyone is going to have different favorites and must-haves, below is a video from KathleenLights that gives a different perspective and may help the budget-conscious.
*FYI- all brands mentioned in her video are CRUELTY FREE