Does The Gym make my fighter better in ranked?

No. Cosmetics and collection only. Ranked uses the same ratings as everyone else.

What should I do first in The Gym?

Keep trainers busy, raise Gym Level, and do not skip dailies. Gameplay improvement happens in Practice Mode.

No. Legacy has its own conditioning. The Gym is the account hub.

Account-wide recruits, trainers, and cosmetics. It is not Career conditioning and it does not make your ranked fighter stronger.

What The Gym does in UFC 6: recruit fighters, assign trainers, earn cosmetic XP — it does not raise ranked stats.