As far as keeping coyotes out of your chicken coop, just make sure you have a good strong latch on the door. How rural are you? That'll make a diff on the coyotes getting your chickens. We are out in the country, and I have been outside at night (I do moon rituals so I'm out alot at night by myself) and heard coyotes sooo close I could hear them growling at whatever it was they were chasing. They were just a few steps across my creek! Anyway, the thing I have the most trouble w/is stray dogs. I have literally gone out to find dead chickens and guineas everywhere. It was awful. I have had to shoot several strays because I caught them eating my chickens. Now, we let ours free range during the day, and now we don't actually have many chickens. We are eating guinea eggs.
Anywhoo, we haven't been able to afford to fence all our property yet, so we just have to deal right now. We are about to start raising meat rabbits, 'cause they'll be more manageable as far as the stray dogs. (now, that's something else you could look into!) We'll get way more chickens after we secure things better and do more fencing.
So, as long as you have a fenced yard, you shouldn't have any problems. Just make sure to put them in the coop each night and lock it up tight. That is often too much trouble for coyotes, and they'd rather go chase a wild rabbit down. OH, and for very little cost, you can install a heat lamp (get one w/ a red heat bulb so chickens don't pick at each other) to turn on in the coop on cold nights. we even do that for our guineas (and they are wild birds). I have never noticed any extra cost on our electric bill due to the heat lamp. In the winter, if you want to encourage laying, just put up a regular light bulb along w/the red one. Keep it on for several hours after it gets dark. Then turn it off before you go to bed. Also, I would suggest looking for a breed called a White Rock, or a White Giant. They are great layers, and typically lay throughout the winter months.
Oh, and if you have a neighbor who has chickens, go ask them if they have any leftover chicken wire you could buy/barter for. If not, it really is cheap to buy. Or you can use a roll of hardware cloth, which is also pretty cheap. If you have any clothesline (again, cheap!) you can even weave your own!
And definitely do the compost thing! Can't believe I forgot that! They will love you for it! Just don't give them raw potato skins. YOu can cook them in the microwave and give to them like that, though.
Oh, and a great book for raising chickens is the Storey's Guide to Raising Chickens. I have that, plus the one for rabbits, and horses.