Dan,
That car is nothing but a pile of junk taking up otherwise useful space in your garage. Being that you're a new guy here, I'd be willing to do you the favor of getting it out of your garage for you to make space for more useful stuff that your wife might want to put there.
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On a more serious note, the car appears to be a pretty choice piece, especially if that paint is still original. Even with a few nicks and dings, paint can only be original "ONCE", and hides no sins! Interior looks pretty good. Everything already suggested are a great start. Brakes, top to bottom are a top priority! Jack it up, pull a front wheel and see if the fronts are drum or disc. If they are disc

awesome. If drum, you need to decide if you want to spend the $$ (expect $75-$350 depending) to refurb the old, inferior front drum setup or use that $$ towards a fairly wide range of good options for upgrading to front disc brakes ranging from around $350 to $1200. If you upgrade, I suggest you go with a non-exotic setup that uses standard, easily available, OEM style off the shelf parts that won't compromise originality, but will make the car safer and more modern feeling. To elaborate a bit on 2+2GT's suggestion, pull all spark plugs, fill each cylinder with Marvel Mystery Oil and let it sit for a few days before trying to turn the engine. Disconnect the fuel line from the carb and from the frame to the fuel pump. Put in a new or known to be good battery and with the coil to center of the distributor cap wire removed and plugs still out and some old rags/towels to catch the spewing oil, turn the key to spin the engine over a couple of times to clear the oil from the cylinders. Drain the old oil and remove/replace oil filter (Motorcraft preferred "NO" Fram or Pennzoil filters) and refill with oil. If you are not comfortable/experienced with pulling/reinstalling the distributor, you will likely be okay with still leaving the plugs out and spinning the motor with the starter in 5 second bursts, 5 or 6 times, taking a 10 second or so break in between, to pump/distribute oil though the system. Install a new set of points and condenser in the distributor and adjust them (we can lead you through this, if needed), install new, properly gapped (.035" I think) spark plugs. Put in a new fuel filter and reconnect the fuel line to the carb. Get a 12-15 foot piece of 3/8" fuel hose and connect one end to the fuel pump inlet (where you removed the hose from the frame and stick the other end into a preferably steel gas can (3/4 full of gas and as far from the car as possible) pour an ounce or so of gas down into the carb by opening the choke plate by hand (air cleaner removed, obviously) and try cranking the engine while pumping/tickling the gas pedal and see if it will fire up. If it starts or tries to start and dies out, repeat the priming process a few times to see if the fuel pump will start sucking gas from the can. If it keeps starting and dying after a couple seconds, you likely need a fuel pump. Check this by removing the fuel line from the carb, disconnecting coil wire and cranking the engine for a second or two to see if fuel comes out of the line. If it starts and runs, don't run for more than 45 seconds to a minute until you drain the old antifreeze/coolant (if there is any) and refill with only distilled water or distilled water/antifreeze mixture (I don't know where you are or the related freezing issues). Never use tap water in a cooling system, distilled only. If all has gone well, you should now be able to run the engine for a bit to see if any ticking/odd noises get better and for possible smoking to subside, keeping an eye out for overheating and coolant flow. If the car will now run, now is the time to remove the gas tank (pretty easy/simple) and have it checked/cleaned or replace with a new one for about $100-$130. My vote is for new. Old gas tank crud can plague you for years until you bite the bullet and take care of it properly. Flush the fuel lines by blowing some compressed air through it and then squirt a whole can or two of Brake cleaner to kind of fill it and then blow it out again. Once flushed, replace the hose portions at the gas tank, under the floor beneath drivers left foot and the piece from the frame to the fuel pump. Now would also be the time to start addressing the brakes. Master Cylinder, wheel cylinders and hoses at minimum. Please keep us posted with your progress and questions. These old Mustangs can be a lot of fun to work on and drive, especially when you're not fighting battles with rust or collision damage.
Happy Motoring,
Gene