Minotaur Totem Barbarian, as you say:

• Level 1: Rage - Advantage on all strength checks and saving throws (which is what shoving or grappling is)

• Level 3: Bear Totem for tankiness reasons.

• Level 4: Sentinel Feat to actually force people deal with you

• Level 5: Two chances per turn to grapple or shove if you really want to

• Level 6: Bear Totem for stereotypical tankiness reasons.

• Level 8: Magic Initiate Druid for Thunder Clap (to simulate Pulverize when not raging), another Druid cantrip of your choice, and then Healing Word for Alistar's passive where he roars and people get healed.

• Level 14 Elk or Wolf Totem to trample over an enemy and knock them prone. Wolf totem does it with no save, but doesn't actually allow you to trample through an enemy like Elk does.

The minotaur race as a whole already has Alistar's E built in with Hammering Horns, which is nice.

Maybe Barb 1/Rogue 1/Barb X so you can grab Expertise in Athletics early to make sure those grapples/shoves stick.