The Browning BPS is an excellent shotgun but out of your price range unless you find a real good deal on a used one.
I see nothing wrong with the 870 express. I have 2 friends that beat the tar out them and they haven't missed a stroke.
It fits the budget and probably fits you better. The Remington has a shorter stock than the Browning. I started with an 870 Wingmaster 25 years ago, still have it. It will be one of the boy's when they get bigger.
Another option is the lowly Mossberg, easily in your budget, been around for years, choke tubes, etc. I have 2 20ga's for my sons, they have missed a beat either. Also simular stock design as the Remington. Maybe not as nice looking as a Browning or Remington Wingmaster but a very sevicable shotgun.
I think either the Rem or Moss. will give you a life time of service without breaking the bank.