I was given 2 bras from my Hospital, specially designed for augmentations,
Isnt it gorgeous?!
Its a compression bra, it was actually really good, And i had a strap/bandage on top, so it would of been similar to that bra you found with that on too.
Check with your ps though, but if you do get a sports bra it should be at least level 3 / high / maximum impact.
It does say its for Breast implants, so i would of though it'd be ok.
You could always get some cheaper ones to start with coz you'll probably change sizes with swelling etc.