The answer is related to the standalone player. Some models are not able to give enough power to the USB port to ensure the correct operation of the external HDD, so in this case you’ll need anyway a powered disk.
Can you post here the exact model? Maybe someone with the same drive can answer you better
Usually a 2.5" HDD doesn’t need an external powering, but again it is related to the standalone.
If you want to buy a product without risks, I suggest to get a 3.5" drive (that need of an external powering). It is more cumbersome, but it will be working for sure.
Remember also that the drive must be formatted in FAT32 to be correctly working with a standalone, and if you get a large drive (1TB for example) you’ll be faced with another problem.
For some reason, Windows will not allow you to format the entire drive in FAT32, but it will allow you to format only 20GB max (if I remember correctly).
There are two possible solutions: creating many small partitions (this can be useful if you want to keep your movie collection ordered in some way for example using separate partitions for Comedy, Drama, or Sci-Fi movies) or using Linux to format the disc.
In fact, Linux allow to format also large discs in FAT32 with no limitations. I really have no idea why Windows doesn’t allow to format large discs in FAT32
To use Linux it is not necessary to install it in your computer, but again there are two solutions: Asking to a friend that already uses Linux, or booting your computer from a CD containing a Live distribution of Linux (for example Knoppix or, better, SystemRescue CD). Once you formatted the disc, simply remove the CD and reboot the computer