Everybody should buy what they want ...
a. Coach guns are going to have short barrels ...but most of them are junk ...in terms of both barrels shooting to the same point, craftmanship, durability etc...and they usually have fixed chokes. A lot of shotguns built or intended for home defense...have no changeable screw in chokes - they're most often fixed with open cyclinder chokes. Stoeger and others make some coach guns - but I wouldn't give a dime for any of them.
b. Traditionally - general purpose bird guns - are going to have 26" or 28" barrels whether they're O/U's or pump guns - and today the trend for many of us is to 30" barrels. In general an O/U with 28" barrels - because the receiver on an O/U is shorter than a semi-auto or pump will be the same overall length as a semi-auto or pump gun with 26" barrels ... So to find an O/U with anything shorter than 26" is next to impossible - unless somebody has cut them down.
O/U's are more expensive to mfg -- to do it right - than pump and semi-auto shotguns...so the market of O/U's under $1,000 is largely full of junk / with the better and stronger guns in the O/U market selling new for $ 2,000 - $ 3,000. You'll find some used guns ( Browning or Beretta - maybe ...) or you'll have to search the used gunstores for a Ruger or maybe an SKB ...and they'll probably be ok, if you can find one .....new, in that price range - you'll only find guns made in Turkey or China probably - with all kinds of issues ( TriStar, Stoeger, Huglu, Mossberg, Baikal, etc ) ...but you might get lucky and get a good one. But I can't with a clean conscience recommend any of the low end guns. If I had to tell you one to look at it would be the TriStar - Cabelas is importing them ...and I think they still have a 5 yr warranty on them ...so at least you'd have that to fall back on. But in that price range - the quality of the steel, etc is just not there....
My opinion about defense vs fighting guns ....is any shotgun can be used for "Defense" ...so if I had to I'd go with a pump gun or a semi-auto in a 26", 28" or even a 30" barrel. It would also give you a gun you could "plink" with or whatever ...especially if it had screw in chokes ...guns like a Browning BPS Hunter model - sell new for around $ 525 or so ....good long term guns. They aren't meant to be a "Fighting gun" like a Benelli M-4 ..../ that's a different animal ....
In my case - I have a lot of shotguns / but my handguns are my primary defensive weapon ..( mine is a 1911 in .45acp --and I practice with it weekly ..) .../ I don't want a shotgun as a primary defensive weapon -especially with only 2 shells in it. I'd want a pump or semi-auto ( with the plug out of it ) with 5 shells in it...if I had to use it for Defense.
But like I said --- everyone should buy what they want /what they can afford.