4TB is a lot of space
You have serious space needs if you are looking into a 4TB external hard drive. This amount of space could contain the complete work and private information of at least 3 people even if they have work which uses moderate-sized files. You're talking about half a million songs! That too in relatively high-quality audio.
Well known brands and features
4TB external hard drives are available in different makes but the more known ones are Western Digital, CalDigit, Seagate, LaCie, ADATA and Samsung among others. These drives have different connectivity options but the most common is USB with the SSUSB on the hard drive end for faster speeds. There are builds that are waterproof and shockproof in case you feel like you might have need for such protection. Even at 4TB the size is easily portable so storing it wouldn't take up too much space which makes it even more convenient.
Internal build types
External hard drives are available in HDD tech or the newer Solid State Drives (SSD). The SSD are faster as they don't have moving parts and use electronic circuits to write and retrieve information, based on the Flash Memory tech that powers our RAM chips too. This lack of moving parts also makes them more resilient over extended periods of use.