For home defense I'd go with the 870 express and spend the rest on quality 00 or #2 ammunition...with an ample amount of # 7 1/2 for clays. A new 870 won't be much over $300 (if that), and the Ithaca 37 will be pushing 3X that amount (even a used one will bring you close to 2X). Is the Ithaca a better gun? HOLY HELL YES IT IS, but that's what accounts for the price difference. I wouldn't dream of tossing the 37 in my trunk for a camping trip, but I know I can huck the Express any ol' place and not worry about babying it. I have experience with both guns, and love them both. I wouldn't get a Wingmaster because while it might be slightly smoother on the action (or so I'm told from a recent question I asked here on THR), but in a home defense scenario with adrenaline pumping...are you going to notice?
Long story short, these are my beliefs.
1) The Ithaca is the better gun at a much higher price.
2) I consider a HD gun to also meet the criteria of a SHTF gun, and I think that both guns would do well in this case.
3) Both shoulder similarly (for me) and have similar safeties, so if you're already familiar with one, you'll more than likely to well with the other.
4) I like the 870 because in a high stress situation, you can slap a round in the chamber and be good to go. If you're not used to a bottom loader, it might be awkward under stress.
5) You can buy an 870 with a 28inch barrel for $300, and buy an 18inch barrel to go with it for $100. $400 isn't a bad investment for a hunting/knockaround gun AND a HG piece.
Oh, and my dad has a 37 that he's shot for 50 years with ZERO issues...NOTHING. I've owned an 870 for 20 years with ZERO issues. I can hit anything with one that I can hit with the other.