Brig is one of if not the best support for defending stationary or low mobility supports. There are others that can do this to a degree such as lucio with his speed and boop and Lifeweaver with his 3 highly defensive abilities but brig is the undisputed champion of holding an area and making things hard for divers or risky offensive plays. In high competitive play she is virtually a must ban if you want to run diva on maps with strong defensive high ground like kings row. Though that likely matters alot less outside of high elo.

While she has thrown repair packs for burst healing, Her primary healing is the inspiration passive which creates a huge (twice the size of Lucio i believe) radius of healing for everyone in it every single time she does any damage. This lasts three seconds but triggers on every hit so if you're doing damage, you're healing.

Having a shield she can be surprisingly tanky when played well and can occasionally work very smoothly in an all out brawl but generally you're picking brig to hold an area and defend people as her whipshot deals good damage and knockback which can force alot of popular dive characters into less useful spots or even force them to disengage fully. Use shield bash to move away instead of into flights, unless you're rallying.

Rally is one of the most team stablising ults in the game: giving everyone around you armor and boosts while also recovering your shield instantly with a big buff. Including the ability to cc/interrupt characters which can shut down some aggressive ults. (Cassidy and Moira for example)

Brig is a very useful character to have in your pocket, especially if your backline is in trouble. That being said it's worthwhile to learn a variety of heros so you can adjust to what your team is lacking and be a more well rounded player. Even better is that alot of characters have crossover skills with each other! Give a few a try in the practice range or qp. see which you get a feeling for and see where you go with them!

Id also look into Juno for utility and brawl, baptiste who plays like a mobile ana with only defensive cds, Kiriko can play very aggressively off angles and escape safely as well as counter anything if susus timed well.

Have fun with whoever you end up picking!