Intermediates
To get under 1 minute, try to memorize 7 OLL and 3 PLL cases.
First 7 OLLs in this link.
First 3 PLLs in this link.
Additionally, the first 10 F2L cases in this link would be useful to know. Do not just memorize them and think how it is done.
General idea of times in CFOP.
Experts
To get under 30 seconds, try to memorize all 21 PLLs, some OLLs, and some F2L cases.
To get under 15 seconds, memorizing all OLL and F2L cases is highly recommended (some can average sub15 without them though). And more importantly, practice look-ahead. Solve the cube slowly and track other pieces. Here is a video.
Other useful things to know would be:
some winter-variation cases.
some COLL cases.
OLL-PLL from other angles.
Super Experts
Practice. Practice. Practice.
Or learn some cases from WV, VHLS, COLL, ZBLL, MGLS, ELS, ELL, etc.
Color Neutrality doesn’t really matter. Feliks Zemdegs is CN but Mats Valk isn’t. However opposite CN is necessary (like white and yellow cross).