Don't get a USB flash drive, get a USB mechanical hard drive. It's much cheaper on a per-capacity basis and fast enough. I'd suggest getting at least half a terabyte (or whatever size drive currently has the lowest $/GB).
I guess my thinking was that I would essentially be only using it for recording a single episode or game and then erasing it after I watch it, so why bother getting all the extra space. Additionally, with a flash drive, one wouldn't have to worry about turning the storage device on and off each time you want to record something.
Do such mechanical USB hard drives also need to be plugged in and turned on all the time when in use or are they to the point where they can be powerded by the USB connection? I have a 1TB external that needs to be plugged into a power outlet seperately, but it's about 6 years old at this point, so I wasn't sure if I'm going off of old information with this.
If it's worth the expense and effort to set up a DVR at all, then chances are you're going to use it enough to be worth getting more than 64 gb capacity.
Conversely, if you want to record so few things that they'll fit comfortably on cheap flash media, I suggest just skipping the DVR entirely because you're (literally) not missing much.
As for whether the drive needs to be plugged in separately, in general, desktop (3.5") drives need separate power while laptop (2.5") drives should be able to run directly off USB. However, some 2.5" drives may need to be plugged into 2 USB ports to get enough amps, or the DVR itself might not be able to supply as many amps as the USB spec says it should. To be safe, you should expect to plug in the drive separately, but hopefully the DVR/drive would support spinning down the disk when it's not being used to save power.
(Alternatively, I'm sure you could find a DVR where you install an internal HD. Then you can be sure it won't require separate power.)
Is there anything important stored on your 6-year-old 1TB external hard drive? If so, then one option you might consider would be buying a new external drive, moving your important stuff to it, then using the old drive with the DVR. That way, when it dies you won't have lost anything important.