I'm getting the 500GB model

I plan to buy all my games physical, only buying digital if it is the only option

Will I need an external hard drive, if so, what are some recommendations?

I just capped out and never bought digital, only expansions.

Ps4 don't currently support external hard drives. Though you can replace the internal hard drive.
All physical games you buy will still be installed on the hard drive, though it's usually pretty fast, you can also easily delete games later (without deleting saved data for the game)
If you plan on getting playstation plus and keeping it for several years, you might want to get a larger internal hard drive. If not, then you might be fine with what you have.

Here is what you do. When you buy a disc, it will install. Play it, and when you beat it, and no longer want to play it daily, you unstall it. The save for the game will remain there, but the large 40GB files or whatever will be gone. Rinse and repeat. If you do this, and don't buy digital like me, you won't even run out of space with a 500GB HDD. 

Thanks for the awesome tip, I'll be doing that for sure

it doesnt support External HD for installing games only media files etc.