You will want better brakes and yes, some suspension and chassis upgrades. It is not a MUST but very desirable. It will depend a lot on the condition of the car you get.
The stock
trans can handle 300 hp, but dont abuse it !!!. Something i'm sure wont happen hehehe. So be prepared to upgrade it sometime.
Sorry to tell you but that engine doesnt look worth it, it is a very basic block, not even forged pistons or at least good iron heads. I doubt it would be capable of 325HP unless they use high compression on it.
Look at DSS, SCAT and Ford for some good block deals. You want at least a block with a decent set of heads and if possible forged pistons in case you have plans for a supercharger.
A ford GT40 crate engine with alum heads sells for around $3,500, but doesnt include intake or carb. But those you can get both from Edelbrock for around $500.
Things that break:
Electronics: wiring tends to have cracked insulation, bad contacts on the connectors. Aftermarket stereo and alarm systems if not installed correctly can cause problems, make sure all wiring under the dash is properly insulated.
Exhaust: Could be crap if the car spent some time near salt.
Body: same problems as above.
Suspension: worn bushings, easy and cheap to replace, a must when buying a car with many k miles.
Disc Rotors: inspect the thickness and look for cracks or "spiderwebbing", could need replacement
Water pump and cooling system: have it checked !!!!
Trannys: AOD or AODE, T5 or T45, both decent on a street car, but if abused it doesnt take much to break them.
5.0s are pretty reliable, the above problems are not 5.0 specific, mostly things to look at.