I have a Rem. 1100 LT-20 synthetic youth gun that fits your description almost exactly. The barrel is 21" but the stock is shortened and it's actually about the same length overall as my 18" 870 HD gun.
I paid $350 for it used, two years ago. For HD, I would rather have an 11-87 since it gives 3" capability, they are also available in 20 ga. youth and I've seen them sell recently for $400.