From Plymouth, effectively the greatest majority of trains will be operated by First Great Western, with a small number of trains running to Bristol & beyond being Cross Country trains. Truro & Liskeard are on the main line, while Newquay requires a change of train onto a branch line at Par.
Despite being on a main line, most trains I tend to take my bike on are small two-carriage ones, rated to carry two bicycles. The high-speed main line FGW trains have a separate storage compartment for bicycles (and surfboards, as I recently discovered when I found I couldn't board the train as there was no space!)
While the Cross Country main line high-speed trains are more "high-tech", with digital name displays for reserved seats, etc. I have to say I prefer the FGW main line high-speed trains. Above all else, this is because of ONE reason: on Cross Country trains, bikes are stored inside the carriages, by the doors.
These trains can carry fewer bicycles, so reservation is essential. More importantly, you're NOT allowed to lock your bike to the train, meaning at each & every stop absolutely anybody can simply wheel your bike off the train. By the time you notice your bike on the platform (if you do) it'd be too late and the train will be rolling out of the station again!
Overall I've found no real issues taking my bike on the train. Typically I simply cycle to the station, buy a
|A lone wind generator on the way to Newquay|
Now there is room for improvement, obviously! For example, it'd be rather nice if FGW could add far bigger signage to the outside of the carriage that bikes are supposed to load in, and have the digital displays at stations tell you at which end of the train the carriage will be. This will save a lot of desperate running to the other end of the train, dodging dismounting passengers while doing so, as it really seems to be a case of pot luck.
Also, larger and more prominent signage inside the carriage asking people not to sit on the fold-down seats in the bicycle area while there are empty seats elsewhere on the train would REALLY help. I've lost count of the number of times I've been standing with my bike all the way from Plymouth to Truro, while one or two people are sat in the bikes area and with a large number of empty seats being ignored by them.