I've had a C12 for 4 months straight, basically because I want to fly. This way, if I'm home, I can get my kids on the bus and my wife doesn't have to worry about it. I'll also get the leftovers in trips this way. The C04 and C06 guys will probably get the last minute short call notifications more than me, since people will tend to call in the morning as sick. Quite a few times the early call guys will do the first round trip and I'll do the rest of the 4 day. It all depends on your availability in the Bucket as well as your availability on duty. If you're on R04 or C04, you can't do a trip with a 1800 duty in and 3 legs until 0100 because of your on call time.
I've seen most of my trips on eTrip prior to the call. A majority of the time I'll receive a "courtesy call" to check my schedule the day prior. It's up to you if you wish to answer the call if you're not on call. CS seems to be fairly good about the "courtesy call", so at least you'll have a warning. The only time I've received a short call was due to a last minute sick call. It's been rare.
It all depends on your Reserve Request and if they'll give you your preferences or not. I've received my first preference every month this year. If you don't want to fly, don't list yourself as a CMF (Call Me First).
The more important question is this. Do you live 2 hours from the airport, or do you live 1 1/2 hours from the airport to give yourself enough time to get on the bus (15 minutes prior to duty in is pushing it) and duty in? I live 45 minutes from the airport and time my departure from home depending on what time I have to be on the bus. The buses leave every 15 minutes, and there's supposes to be an Express 4 times an hour in between the large buses, but not always. I've flown with an individual who lives in CHA and sat at home on reserve. It was definitely pushing the envelope. It's all up to you.
Hope this helps.