That's something I forgot to explain! PCSX-R actually loads the TOC or CUE files "silently", as in, just clicking the corresponding bin file will work because the emulator finds that itself. That's partly why you can't have the TOC and CUE in the same folder together because it can't prioritize between the two. (At least not yet; it's bound to change in the future.)
So yes, you'll still need the TOC in the same folder as the game. =P In Vib Ribbon's case, I think that may just be a compatibility issue; other games that I dumped with CUEs, or converted TOCs afterwards, seem to be working fine.
Both CUE sheets and TOCs can be opened in a text editor, so if you decide to rename your dumps, you will need to manually rename lines in the TOCs to match your dump's file name. Personally I recommend all caps for both so there's less case-sensitive issues between running game images in Windows and Linux.
For instance, this is what my cue sheet for Spyro the Dragon looks like :
It doesn't have any audio sessions recorded, so it's just one track. I actually run the game without the CUE sheet because of that and everything's been fine so far, from start to finish!
FILE "Spyro the Dragon.bin" BINARY
TRACK 01 MODE2/2352
INDEX 01 00:00:00
This is what you'll expect with games that use CD Audio in TOC format. There's an entry for every audio track so the emulator knows where to look for audio sessions.
Easy enough, no? =P
// Generated by cue2toc 0.4
// Report bugs to <email@example.com>
DATAFILE "VIB_RIBBON.bin" 01:29:00
AUDIOFILE "VIB_RIBBON.bin" 01:29:00
AUDIOFILE "VIB_RIBBON.bin" 04:06:00 04:08:00
AUDIOFILE "VIB_RIBBON.bin" 06:40:00 06:42:00
AUDIOFILE "VIB_RIBBON.bin" 09:12:00 09:14:00
AUDIOFILE "VIB_RIBBON.bin" 11:47:00 11:49:00
AUDIOFILE "VIB_RIBBON.bin" 14:34:00 14:36:00
AUDIOFILE "VIB_RIBBON.bin" 17:07:00 17:09:00
EDIT : As for the right image mounting application, that's something I haven't looked into in years, so I don't know how much has changed since then. There are plenty of them to choose from in the Software Center, though, so it couldn't hurt to try any of those first.