I want to upgrade my early 2015 MacBook Pro storage

Good questions all. First, I suggest that you reformat it if needed. Second, delete any maintenance software that is on it. These almost always are problematic. Connection should be with a USB cable. They are usually provided by the vendor. Do not also use it for Time Machine. Time Machine should have its own dedicated disk. Make sure that the disk is large enough to accommodate your storage needs. To install the operating system on the new disk, go to the Apple App store (or Apple's web page), do a search and download it. I recommend that you use an Ethernet connection as Wi-Fi often fails. These downloads are too large and corruption often occurs. It will likely take 45 minutes, more or less. Then installation can take another 20 or 30 minutes with several automatic restarts. At the end, the external disk will be set as the startup disk. Then you may wish to copy over your other files to the new disk. As to the brand, I assume that it will be fine. If not, it will be covered by warranty, so no worry.

If you can afford the SSD then by all means buy that ... your money; your choice. But consider, just how much speed do you need for large amounts of data storage?

HDD tech is mature and now days even very large units are cheap compared to the same size SSD.

If you intend to use the space for storage only, an OS on the drive is a waste of space. If you plan on booting from external, SSD is the way to go. But for pure storage, an inexpensive, comparatively anyway, HDD is ideal.

Pretty much any hard disk drive or solid state drive can be attached as external storage.

I agree. However, most of us would recommend using an SSD since it will be much faster. I'm assuming that you will be using the disk as your startup disk, so you will need to install an OS on it.