I think that rather than using feats or something to bring everyone else up to the minotaur, you should consider giving the minotaur player character equivalent racial bonuses to the other races. I think that deciding to play a minotaur should be more about flavor than mechanics. I won't have a PHB in front of me until later tonight, but looking at the minotaur in basic D&D I could see something like this being reasonable.
Ability Score Increase: Strength +2, Constitution +1
Age: Pull up some info from an earlier edition.
Alignment: Generally chaotic evil
Size: Large
Speed: 40 ft.
Languages: You can speek common and abyssal
Darkvision: 60ft
Charge: If you move at least 10 ft. in a straight toward a target and hit with a gore attack, the target takes an additional 2d8 piercing damage. If it is a creature, it must succeed on a (8 + your proficiency bonus + your strength modifier) saving throw or be pushed up to 10 feet and fall prone.
Natural armor: It is difficult to make armor for you, but you don't need it. When calculating armor solely using dexterity modifier, you add an additional 4 to your AC.
Labyrinthine recall: You can perfectly remember any path you have traveled.
Gore: Strength based melee attack. +Proficiency and strength modifier to attack. Reach 5 ft., one creature. Hit: 2d8 + strength modifier piercing damage.
Weapons: You have proficiency in heavy weapons (which are wielded one handed?) and spears. (You can only wield these weapons?).
Possible Subrace: +1 to wisdom instead of constitution.
Because of the large, strong nature of the creature, I could also see adding 1 additional damage die to heavy weapon hits, and possibly making the maximum strength score a 22. Neither would be necessary to have an enjoyable time playing a minotaur (this is more about flavor than mechanics), and they might imbalance things slightly. The ability to wield a heavy weapon and a shield might be enough of an advantage, and large creatures double the weight that can be pushed or carried over medium and small creatures. As a DM, I would choose the 1 extra damage die for heavy weapons over raising the strength score as it is not as necessary to work within the rest of the rules framework.
We have a half-gnoll paladin in our current campaign. I allowed it because he was the son of that player's human druid and a tribe of good gnolls (based on gnoll aasimar) in our previous campagin. Right now he is a little short on racial trait bonuses because the gnoll statblock in D&D basic does not give much to work with. He got +2 strength, +1 dexterity, proficiency in intimidation (from half-orc), darkvision, gnoll language, and attack someone else as a bonus action when he fells an opponent. I think that is less than what most races in the PHB get. He has not minded any small difference from fewer racial trait bonuses. I guess what I am suggesting is that you not make the minotaur PC better than anyone else mechanically. Playing a special race is special and its own reward. The bonuses for playing that race should be the same or slightly less than the other races in my opinion.