First, thank you for choosing the AR-15. Enjoy your stay. Please study up over at m4carbine.net they'll get you filled in. Join, study up, then post after several hours of reading up on "the chart", TDP, mil-spec, 4150/4140/11595E, HPT/MPI/shot peened, staking, buffer weights, the A5 stock system, gas system lengths, etc. After that, confirm your knowledge via a well-thought-out post, explaining your needs, budget, and what state/country you live in. They'll give you a lot of stuff to research/gaze at/ponder, and help you choose the best rifle for your needs.
If you have $1500 total? PSA 16" patrol carbine with Aimpoint PRO for $1000 total. Top of the line optic, mil-spec carbine.
If you want a gun alone for $1500? Build, you'll get more for your money, and get exactly what you want. Just put a standard mid-length 16" barrel in to start, very effective rifle set up. Use an A5 stock kit and a Spikes Tactical Enhanced LPK. Any decent lower from Spikes Tactical, CMMG, PSA, etc. on your gun store's shelves will work. The upper? I'd advise a PSA full-auto, mil-spec BCG. You want mil-spec. Don't dick around with the crappy gun show parts, and study up on what the true mil-spec is. Know it, it is the standard to compare everything else on the market to. For a fore-end, go with either Magpul MOE handguards or a Troy Industries Alpha Rail (13" variety with an integrated sight). I'd advise a Vortex G6A2 Flash Eliminator, or an AAC Blackout 51T muzzle device. Go for the AAC if you want to mount a suppressor (AAC is the way to go in centerfire suppressors), the Vortex if you don't need a suppressor mount.
Regardless of whether you buy or build, add a Blue Force Gear VCAS Sling. Buy four 30 round PMAG's (enough for any standard carbine class, as well as your defensive loadout, just keep ammo on stripper clips). Buy a Blue Force Gear 10-Speed Chest Rig.
Last I checked, that can all be put together for under $1500, easily. Save up a few hundred extra, and find a carbine course run by a reputable and well-known professional. For under $2200, you ought be able to find a carbine course as well as set up your carbine and acquire adequate ammo for a course (varies from 500-2000 rounds, depending, you can get 2k M193 ammo for under $600).
If I'm not mistaken, the rifle/chest rig/magazines/sling totals out about $1200. The ammo (maximum for a class) is approximately $425-450 (1500 rounds or so). That means you have about $550 for a course. After said course, you'll (hopefully) be competent in the operation of a carbine for defensive needs. You'd do well to put at least 1,000 rounds a year through the gun, to keep your training up (try to shoot monthly if not more). On that schedule, you'd need to replace the barrel somewhere around 12 years from now (the barrels cost anywhere from as low as $175 from Palmetto State Armory to almost $300 via BCM). You'll have to replace the bolt every 3,000-5,000 rounds or so (it'll start having issues, you can sometimes rebuild the bolt and alleviate said issues, I carry a complete bolt at all times), and the carrier ought be replaced with each barrel (wear characteristics show this, just buy a complete mil-spec BCG from PSA for about $110-135 depending). Your buffer spring ought also be replaced every 5,000 rounds or so, cheap to do if you're shooting that much ammo. Aside from that, the gun doesn't wear much. Eventually, your trigger pins will wear the holes larger after many thousands of rounds, that isn't too much of an issue generally. If you can afford to fire the many thousands of rounds through your AR that it takes to wear it this far, you can afford to replace the parts.
I'd advise against proprietary designs like the Colt 6940. While quality, they aren't easy to find replacement parts for (barrels in the 6940, for example).
Good luck in your AR-15 adventures!