[shortwave]

This question is no different then someone asking "what pistol should I buy for SD,CC" etc. with a budget of xyz.

You've been given a few good options including the Mossberg 500 or the Remington 870.

IMO,either would do and it would depend on which felt more comfortable in your hands. Check them both out. Shoulder them, see which safety set up you prefer and if you know someone who may own both, see if you can shoot each.

Too, there are a lot of excellent used shotguns on the market as well.
You can pickup a nice Rem. 1100 in your price range and it may already have the slug bbl. on it. Which is what I use simply cause it's the shotgun I've shot for 35+ yrs. with thousands of rounds downrange and know it best. It's five shot, a little heavy but makes for easier follow up shots. Might be worth your looking at.

Whatever you choose...practice ...practice...practice. Your life may depend on it at 0300 in the morning, pitch black and you don't have time or lighting to be hunting your safety.

One more thing, everyone has their own opinion on building their own SD shotgun. Some like to hang all kinda cool looking do-dads and bells-n-whistle's on them... IE slings, pistol grips, heat shields, door knockers etc.
Again, my opinion is streamline things as much as possible. Hanging things on a SD shotgun only increases weight, width, length or height which increase's the chance of the shotgun hanging up on something and decreases its mobility.