Ok, you have a few things going on here:
There are performance differences between ext4 and NTFS, but you will be more limited by the performance of the Pi than by the file system. In case it matters, ext4 allows more weird characters than NTFS within filenames (like slashes and question marks), so that would be my pick.
Types of hard drives
Basically, you need to choose between a spin drive or an SSD. For the same price, spin drives offer a lot more storage and longer life, SSDs offer a lot more speed and use less electrical power. SSDs tend to have a shorter lifespan than spin drives, and for a webstorage application, space and reliability are generally more important than speed, so I'd go for a spin drive.
Hard Drive Specs
If you are going for a spin drive, look at the read and write speeds, and make sure the drive is at least 7200rpm.
On the Pi, you are kinda limited to USB. There is a wide selection of USB drives out there. Just keep in mind that, on the Pi, the Ethernet and USB are controlled by the same bus.
For a webstorage application, you may wish to setup a RAID array. This will allow you to use several hard drives as either mirrors of eachother (for redundancy) and to spread your files around (for speed of access). You do have 4 USB ports on the Pi3, may as well use them.