Usually a rewritable disc contains more errors after the burn, and some standalones are not able to correctly handle a disc if it contains too much errors. In some standalones, moreover, the firmware is purposely locked so you can’t use a burned disc, but only pressed media.
In this latter case the player can be “cheated” using a little trick: burning a DVD [B]+R[/B] disc changing the booktype in ROM, so the player see the burned disc as if it is a pressed media. Very often this is sufficient to make an usable disc.
Regarding the external discs, what I meant is to buy a standalone with an USB port, so you can use a hard disk that can be plugged in the USB connector and you can play movies on your television directly from the hard disk
Just to give you an example about external discs, take a look here
Another interesting alternative are the multimedia hard drives (see here an example)
I hope that this can help