Basically the post important thing is keeping a good set of backups which you will be able to access in the future for safe and faster restore times. Then, there is media access, time shift, recordings, playbacks, etc. Also, if you ever decide to test mutliboot, the faster the internal drive chosen, the faster the receiver will boot. The faster drive means more heat, but I haven't had any problems with my 3.5 drive using a laptop cooler under the receiver. Runs cool as a cucumber.
Size will depend on your preference. I still have an internal WD black label 750 gb in my receiver which is more than sufficient for me, plus four 2 tb external 3.0 usb Seagates backwards compatible to 2.0 which is over kill.
Yes, I would add a hard drive, you won't regret it.