If I am getting an external hard drive for my PS4, should I use it exclusive for the console, or will I be fine for multi-use?

After getting tired of constantly uninstalling and reinstalling games on my PS4, I am finally upgrading my space on my PS4 with an external hard drive... yea! However I am also looking at upgrading an older 500GB Hard drive that I primarily use for backing up my computer/have a few movies on..etc.

My question is that, Should I get separate hard drives for each purpose, or will I be fine with one hard drive with slightly larger space? It would be primarily used for the PS4, but I would link it in with my computer every month or so to back that up.

Also, any suggestions on what is best to buy would be welcome. I am thinking either this 4TB Seagate that's on Amazon, or This 4TB WD external that Best Buy has on sale..

Thanks in advance for any advice