The local auto parts store will sell you a flush kit with instructions and the flush chemicals. The flush kit is about $5-$7, the flush chemicals are about the same. This will flush the whole cooling system, which is a good idea.
Carefully look the cooling system over for swollen or deteriorated hoses, rusted clamps or obvious leaks. Write it down so when you make the trip to the auto parts store you get everything you need in one trip.
Plan on spending some $ for 2 gallons of new antifreeze. Get the full strength stuff, buy the mix and you are paying $$$ for water. Mix it 50% antifreeze and 50% water and you will be good. The Chilton's shop manual says the cooling system holds 14 qts, so that's 3 1/2 gallons of mixed antifreeze if you have a dry system.
What typically happens is that there is clear water left in the system after you flush it. That means you need to add 7 qts of pure antifreeze (not antifreeze mix) to the radiator. I recommend that you remove the bottom hose from the radiator and drain the water from it. Reconnect the hose and then add the 7 qts of antifreeze, it may not all fit. Once the engine gets warm, the coolant level will drop, so add the rest of the 7 qts of antifreeze and more water to top it off. Check the coolant level after you have run the engine for 30 minutes or so. This will get all the air out of the system and allow you to top off the system with water.
Don't forget to empty and refill the overflow tank with the 50/50 mix to the proper mark. It holds the extra coolant that heat forces out of the radiator. When it cools off, the vacuum inside the radiator sucks it back in. After a while, everything balances out, and the radiator has the right amount of coolant and the overflow has the right amount of excess coolant.
You probably will have some antifreeze mix left over, just keep it away from cats and dogs. It is poisonous and animals will drink it like soda pop. Killing your favorite pet (or your neighbors) isn’t a good thing. This means you need to thoroughly wash down your work area when you finish to clean up all the traces of antifreeze.
A new thermostat is a good idea, but the lower thermostat bolt can be hard to get to. Make sure you have the tools to get to it before you purchase a thermostat. I have a 1/4" drive, shallow 1/2" universal socket and it is the only tool that makes the job easy. If you change the thermostat, you will need some blue silicone sealer for the gasket area.
Plan on spending $20 or so on a Chilton's shop manual. It is the best tool investment you can spend on a Mustang. You may not be able to do everything, but you can do a lot of the work yourself and save major $$$.