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.

The wall is opaque but doesn't otherwise stop attacks.

Since the wall of fire is opaque, creatures inside can't be seen. Thus:

When you attack a target that you can’t see, you have disadvantage on the attack roll.

(PHB, p. 194)

This means:

• Melee and missile attackers make their attacks at disadvantage.

• Creatures on one side of the wall may roll a Dexterity(stealth) check to become hidden to foes on the other side of the wall, requiring attackers to guess which locations to target with their attacks.

• Nothing in the spell description specifically says that making attacks through the wall will inflict damage on the attacker.

• Nothing in the spell description specifically says that grappling or shoving are affected.

• However, the description of wall of flame does say that a creature who "enters the wall" takes damage. A DM could quite reasonably rule that grappling, shoving, and making melee attacks with some weapons (short ones) constitute "entering the wall", and impose damage in those cases.

• Any spells that target a creature or point that the caster can see cannot target inside the wall of fire.

• Spell effects extend through the wall (the description of wall of fire doesn't say that they don't), so spells that affect an area that originate from outside the wall can affect creatures inside it normally.

• Note that many spells that are attacks (for example, fire bolt), don't target a creature the caster can see, just one within range. So these spells can be used against creatures inside the wall, but, just like missile attacks, they will be made at disadvantage (or just miss outright).