Welcome to the Forum. You can pretty much use any shotgun for deer, but some models are better designed for it, at the expense of being suitable for other tasks - but that can also be remedied. My advice is to keep it simple and get a 12 gauge pump gun from one of the major manufacturers. You can't go wrong with a Remington 870, but others are fine as well and the bottom ejection of the Browning BPS appeals to some.
If your only intention for the gun is to hunt deer, get one with a slug barrel, which will probably be about 20" with open sights built in. Now that you can use a rifled shotgun (sort of an oxymoron, eh?) in MA, which is where I assume you are, else you'd be looking for a rifle, you might as well go that route. You can also mount a scope or dot sight if you like.
If you decide you want to use the same gun for wingshooting you can get a second barrel, maybe 28" and smoothbore with changeable choke tube, and then you'll be set for hunting just about everything that's legal in MA. Changing out barrels takes maybe two minutes or less.
Unless you really want a new gun - and for something like this there's really no reason to, take a drive up to Kittery Trading Post where they'll have a variety of used guns that fit that description for less than half of your $700 limit. You can use what's left over for that second barrel and probably add a scope and a bunch of ammo to practice with as well. Handle them all and pick the one that feels best to you.
Although I have a number of high-quality double guns, I keep a battered 870 Express around for duck hunting on the theory that if it's too nice to use as a canoe paddle, it's too nice to have in a duck blind. It's served me well for more years than I care to remember.