What you can pick up a used shotgun for these days is your best bet. It is true when they say they don't make them like they use to because in terms of material, they don't. The older 870s, 500s, Ithaca 37s and Stevens were designed to survive a couple of wars and last you a life time. I can't believe you can still pick up a mint condition one up from a dealer no less for around $250-350.
If you want cheap and new I would suggest a Maverick as someone mentioned above or a Stevens. They are in that $300-350 price point. I would chose one of these because they are domestic as in North American made and in theory have a bit more QC and better warranties.
If you don't mind a Turkish gun, I would add guns from Yildiz, Churchill, Uzkon, ATA, Sinsinati, Hunt Group, Winchester and Hatsan to your list. Hunt Group is a bit more expensive averaging at $600 but at that price you could get a new Stoeger, almost a Browning BPS and for sure a 500, 590 or 870.
But in the sub $400 Turkish pump category my first choice would be the Winchester SXP because of its release assist, AR style bolt lock up and standard Invector Plus chokes. American company, specs and standards... just made in Turkey. My second choice would be the Hatsan only because they have slowly built a reputation for no nonsense reliability and my 3 choice would be the Revolution Armoury. Shocking but true, RA is my third choice because they are chasing the mid range market so they are bringing it quality guns from Turkey to compete with companies like Hatsan and based on what I have been hearing from other forums, their customer service is stellar and I am sure if I had any issues with my RA, my experience might just move their ranking about Hatsan's. Did not have to deal with their CS yet and I hope that I don't have to.
The sad truth is that I own atleast one gun from almost each of these companies because after giving up buying expensive guns, like a crack whore, I am hooked on the cheap stuff. I have mucho buyer's regret for most cheap shotguns except for the 3 I listed. I am giving the largest props to RA because I picked up a Nickle plated, walnut, chrome lined barrel with Mobile chokes new for under $400. Bravo RA because the next closes shotguns with those specs are the Rem and Mossy Marines and they are $699 and don't have interchangable chokes. Hope that helps.