I actually have both an FZ-1 and an FZ-10... it's not that I'm that huge of a fan of the system, but I originally got the FZ-1 for cheap and then when the HDD (and later, USB) adapter came out for it, it was clear that the FZ-10 was going to work better with it because you could hide the USB under the top-loader's lid.
I wouldn't worry too much about the FZ-1's attached power cord honestly. If it ever frays, you can always just splice on a new one. Might not look the absolute best, but if you're at all handy with electronics it's a very very easy fix. Nor would I worry about needing a disc to access the memory manager, because the 3DO is from a pre-modchip time and happily plays backups. Worth thinking about the fact that the tray could theoretically have a problem on it though, like you often hear with 1st model Sega CDs (though to be fair, I haven't heard that complaint much about it, but it's still theoretically possible)
The FZ-10 is nice in not needing the disc though if you're trying to go all original, and if you're looking to do the USB upgrade it's going to look much nicer than the Goldstar or the FZ-1, so that's something. In my opinion too, it looks more like a game console. The FZ-1 looks like stereo equipment, which makes sense given how they marketed it at the time, but to me I don't necessarily like it.