A $50 HDD is very small currently (and refurbished), so I'm going to throw that silly figure out & replace it with $100-150, a 2TB drive.
Family videos: Simple 1080p video (not 3D, not multiple angles, etc) is 16GB/hr (on my camera, YMMV). That's just over 100 hours on a 2TB drive. With kids (especially kids in plays/musicals!) this doesn't go as far as you might think.
DVD Collection: Figure 2GB/movie = over 1500 movies at low-def, but let's be realistic, this doesn't look great on a 50"+ TV. HD compressed movies are 10-20GB/movie (IME, YMMV) so we're down to 100 movies.
But wait! You said both on the same drive, so cut both figures in half. Oh, and for 2-3 times the price. Most of everything else you said was spot on, but your mistake was suggesting $50 was enough for storing a "life worth of fotos, videos and [movies]". There is no single HDD big enough for this task at current settings, much less when the industry takes its collective heads out of its collective *** and realizes 1080p isn't all that great - just better than what we had.