We raise and butcher our own chickens and I have learned to very quickly break down the whole chicken into parts. Most of our chickens are cut up into pieces, but about 1/4 are left whole for roasting.
With whole birds, I simply roast by sprinkling inside and out with salt pepper, stuff cavity with herbs, put in roasting pan (I don't cover or use water because I love crispy skin), and roast at 375F until done. This takes about 1.5-2 hours, depending on size. I agree about the thermometer, it makes life a lot easier. Once roasted and eaten, I save all of the bones and make stock. I often freeze the bones until I can make a huge batch at once.
When cutting the birds into pieces, I start with the chicken breast side up and a sharp knife. I remove the breasts (boneless, but skin on) by cutting along the breastbone and then along the ribcage. Then I cut off the wings (tiny tips are saved for stock), and cut off the whole leg (thigh and drumstick), and am left with the back, neck and ribcage for stock. The wings are then cut into two pieces and so are the legs, by cutting through the cartilage in the joints, not the bone. Cutting through the joint cartilage is not like cutting through hard bone and after doing it a couple of times, you will easily find the "line" in the meat that when cut through will go straight through the joint. I know that it's probably hard to visualize when reading this, but YouTube has quite a few videos that could help you out. Since we have many chickens, I freeze the pieces in groups of wings, drumsticks, thighs, etc. and use according to the dish I want to make. There are way too many possibilities to list here.
My main point is that nothing, other than the guts, goes to waste. All the bones are saved after our butchering and after every meal we make with bone-in pieces. So, if we have drumsticks for dinner, the bones inside are frozen until we've saved enough to make stock. Try to cut up a chicken yourself, it's fairly easy and quick after practicing, and you really can't destroy the meat, since you can always make soup out of a jumbled up practice chicken.