You might be told you need new head bolts, but I don't think that is necessary if you use the 80 model bolts. At some point, FoMoCo did go to TTY bolts, but not then.
You might also find the Mustang cam is a bit more aggessive, and could be a 'swap in' for a bit better performance. I do not know the lift/duration etc by year to say. It would definitely bolt in, but if you do swap, you'd also have to swap the followers and keep them in the same spot on the cam. At least I'd suggest doing that as they 'wear into' each other over time.
Both years had distributors, so you should be able to swap your 87 right into place.
Do replace the cam belt as you don't know the 'time' on the old one in the Mustang, or yours may be due for a change. Worth the $12-15 for a new one & peace of mind.
You will need a cylinder head gasket, and an intake manifold gasket if you remove your intake while doing the head swap. The exhaust manifold was not fitted with a gasket at the factory, so if you retain your head, you can retain the exhaust manifold in place without removal, so no gasket necessary.
I'd also replace the thermostat with a Stant, Motorcraft or Robertshaw, OEM quality part. No hecho in Ch*na junque. Not worth the few dollars saved, IMO. And both upper & lower radiator hoses, and make sure the heater hoses were good. Spin the water pump to check for gritty bearings, they are not expensive. New filter along with an oil change, 50/50 on coolant:antifreeze. Fill 'er up.
Take a look at your valves while you have the head off. The color of each valve should indicate condition, and the intakes should all be the same color, as should the exhaust. You can check for leaks using liquids with the head upside down. The head should hold liquid without leakage into the exhaust or intake ports. It's easier to do this now rather than later. You can remove the followers, the cam, and pull the valves if you want a good running engine. Check the valve seat and tulip seating area for uniform color and match. You can lap the valves using some compound to improve seating at little cost in time and effort, and have the chance to install new valve stem seals. Cheap work now, but costly later.
tom