If you are moving your HDD a lot, preferable ang external mobile HDD. No hassle, as no need to bring the AC adapter, if there is one.
If you seldom move your HDD (between TV, NMT, PC), then preferable ang external 3.5" HDD (w/ AC adapter).
If you are getting an internal 3.5" HDD, better get the sata3 HDD. You will need a branded enclosure preferably with USB3 port. If getting a complete external 3.5" HDD package, advisable to get the USB3 capable unit. Most likely the internal HDD is sata3. Even with USB2 connection to the desktop to transfer files, may difference pa rin. What more if straight sa USB3 port for data transfer.
On 3.5" HDD, I suppose the sweet spot (price to capacity ratio) right now is 2TB. With 3TB, you have to make sure your device/s is capable of recognizing it.
That's my reco.