Yes, that's almost (but not quite) correct.
Creating the wall of fire as a ring means everyone inside is going to take damage, yes. However, it's better than you're thinking, because they don't get any saving throws!
The saving throw is only for anyone in the area of the spell when the wall of fire first appears:
When the wall appears, each creature within its area must make a Dexterity saving throw.
That's the only time the spell grants anyone a saving throw. Since spells only do what they say and no more or less, and only grant saves when they say they do, nobody gets a saving throw for any other part of the spell.
Further, the area doesn't include the space surrounded by the wall: the area of a wall spell is only those spaces the wall itself actually occupies — everything surrounded by the wall is just “a bad place to be” (especially for wall of fire). And notice that the save is Dexterity: it's for partially getting out of the way of the forming wall, not for partially resisting the damage (like a Con save would indicate).
So the short version: you cast the spell as a ring with the damage side in, and everyone standing exactly where the wall forms takes 5d8 damage or half on a Dex save; meanwhile anyone surrounded by the ring takes no damage immediately, but will start taking 5d8 damage (no save) at the end of their turn, every turn, until the spell ends or they exit through the wall (taking another 5d8 fire damage, no save, for the effort).
One last point: Careful Spell metamagic (which someone mentioned in a comment) isn't very useful for a ringed wall of fire. All Careful Spell lets a sorcerer do is let a chosen creature automatically succeed on any saving throws the spell grants — it won't protect anyone surrounded by the ring, because they're not getting any saving throws. You could give a friend who happens to be standing right where you want the wall itself to form an automatic save (for half 5d8 damage) just when the wall comes into existence, but that's it.
