I'm not sure there are many rifles that meet *all* those requirements. I think you might have to give up either light weight, price, or hunting caliber. Plenty of guns meet all but one of your requirements, but meeting them all is tricky.
Addressing them one by one:
Guns that are on the lightweight side include a lightweight AR (pencil or lightweight barrel, 16"), Mini-14 (not Target) or Mini Thirty, Kel-Tec SU-16, Remington 7615, lightweight AK in 5.45x39, lever-action in .357, FN PS90, plenty of others, but rules out a number of the hunting-caliber guns. It also rules out the SKS, which is rather big and heavy.
Able to take high capacity mags
Most anything listed above, except not many lever-action magazines are detachable.
Be useful for hunting, but has more of a tactical look and feel (handgrip would be nice)
This tends to argue against the .223's, since it's only marginally powerful enough for deer hunting (you can hunt deer with it if you choose the load carefully, get reasonably close, take only good shots, and aren't hunting the bigger deer species). In a survival situation or in experienced hands, .223 is certainly sufficient for hunting, but is not the ideal caliber for a first deer gun.
A sufficiently accurate AK in 7.62x39mm would work (154-grain softpoints are a decent deer load), *if* the accuracy in your hands is sufficient.
A 6.5mm or 6.8mm AR, one of the rare 6.8mm mini-14's, AR-10, FNAR, M1A, etc. might be well suited for hunting, but many of these can't meet your weight or price criteria.
Be short enough for home defense if necessary
In the HD role, pretty much any 16" barreled carbine would meet the length requirement given an adjustable stock (or a fairly short fixed-length stock), and .223/5.56mm shines in this role.
Unless you live in a masonry-faced house or are pretty isolated, the hunting calibers will pose more risk of exiting the structure than .223/5.56mm.
A decent AR is very durable, certainly as much as a mini-14, and far more durable than a typical pump-action or lever-action. They are also quite reliable if they are put together right and occasionally lubricated; cleaning isn't nearly as important as oil is, just as with the AK.
have a cartridge that is versatile and widely available
That may rule out 5.45x39mm and 6.5mm for you. 6.8mm should be available locally, but it is not as ubiquitous as .223/5.56mm or .308.
be under or around $500 new or used
Ay, there's the rub.
The only thing you'll typically find under $500 is a Romanian AK in 7.62x39mm, a non-Russian SKS, a lever gun, or perhaps an older used mini-14 if you look around (but be aware that serial numbers before 580-xxxxx are typically less accurate than the newer ones).
You can get a good AR for $600 or so, possibly less (the Smith & Wesson M&P Sport has a good reputation for a basic carbine).
I've seen low-end AR-10 type rifles for $800ish, if I recall.