My husband and I are in the process of raising up 15 cornish X chicks now as well as 7 barred rock "filler" chicks that got thrown in the box for warmth. They are sort of like people describe....not much for personality, you can see them getting bigger each day, and they are pretty lazy, but when the mood strikes they get up and play with each other, and run around like normal chicks do. The key is to give them as much space to do their thing as possible, and space the feeders and waterers out so they cant plop down and eat and then just turn their head to get some water. Make them move around and you should hopefully be able to avoid the leg and breathing problems, at least for a while. If you do start to see these issues, switch them to a 12 hour feeding cycle, 12 on, 12 off. This will slow their growth rate and give their little hearts and joints time to catch up to the rest of their bodies.
We have them in a large dog pen enclosure in our garage bottomed with a tarp, and with newspaper and shavings down for them to play in, as well as a covered area for them to snuggle up together. They are only dirty if you don't keep an eye on their bedding, and it does need to be changed every other day to keep them happy and sanitary. They are meat birds, they eat A LOT, hence they poop A LOT...so constant attention and a big run area is key to keeping things manageable if they cant be allowed outside due to cold or weather, etc.
As for the dispatching, I'm making my husband and brother-in-law do it this time. Last spring, we had several cockerels that we couldn't find homes for, and I got the unpleasant job of doing them in, as well as plucking and dressing them. Plucking and dressing isn't so bad but the guts are pretty stinky. To kill them, I used the under the arm, and yank down method of breaking their necks. It worked, but I dont recommended it unless you have a cast iron stomach. Use the hatchet or a cone, it's much easier on you.
Good luck!