http://www.sheldonbrown.com/rim-sizing.html
The 'c' is a holdover from an arcane European system of wheel/tire diameter and width combinations. There was an 'a', a 'b', a 'c' and a 'd' once upon a time. The other three standards have largely or completely disappeared, merged into other newer sizing systems and been replaced by the modern E.R.T.R.O. standards and I.S.O. standards.
Your rim's tire bead seat diameter is 622 MM or 24-1/2". The tire's O.D. is approximately 700 MM or 27-1/2"-27-9/16". The rim's O.D. and the tires actual fully inflated O.D. will vary slightly by manufacturer. tire size and type, etc.
If your current rear road tire is smooth or if it has a slight tread pattern of some sort it is probably just fine for a few weeks of indoor training.
Doing 30 minutes to an hour or so a day over 30 days will not wear down the tire much provided you do not try holding daily FTP/VO2 Max test sessions or do repeated sprint accelerations. Even if you do put a little heat into the tire you can go into cruise mode and cool it down...sorta like NASCAR. Don't slip the tire on the trainer's roller.
That brings up the trainer's driven roller pressure against the tire. Get your tire up to around 105 PSI or so...check the sidewall for maximum pressure. Make sure there is enough pressure on the roller to eliminate tire slippage. Grab the tire and give it a few hard jerks back and forth and try to feel the trainer slipping. No need to over-do the roller pressure, but it does have to be snug enough to keep your tire from prematurely wearing.
To much roller pressure and you'll deform the sidewall enough to cause heat buildup. You want to avoid that, also.
Nigel's advice on going near max. pressure helps keep the sidewall from being overly flattened. I usually ride my sew-ups around 110 PSI on the trainer. A very hard rear tire on a trainer will also point out a rim in need of truing, and out-of-round or cord-damaged tire, etc. Let any vibrations be a pointer to possible needed adjustments or maintenance.
Ride an easy warmup and then do 10 minutes of pretty good riding. Stop and check the tire for temperature. I may be just a little warm, but it should be nowhere near 'hot'.