I am extremely new to chickens, and I have a few questions that I can't seem to find a clear answer to.

1. How many nesting boxes do I need for each hen? Roosts?

2. If I attempt to use chicken wire (3' tall), will they fly out and will they return each night? (Dog across the road loves to eat baby rabbits!)

3. I live in Minnesota, how well will they over winter?

4. What breed would be good for a beginer (obediant, good eggs, and fun to look at?), and given the situations above?

Your help will be greatly appreciated. Thank You!

Welcome to the wonderful world of chickens!

To answer your questions...
Nestboxes should be provided so there is about one for every 3-5 hens. If you see a few chickens in one box, a couple more should be added. Roosts should have enough space so each hen is comfortably fit. More space is often neccessary because the "top" hens often push the lesser ones off.

If there is plenty of room to roam around, a 3' fence should be okay, and they won't fly over it. If they are crowded, they will fly out, and may not figure out how to get back in. The dog will have a nice snack.

Chickens seem to survive the winter months pretty well. I live in Wisconsin and only loose a few older ones in the winter. During the colder nights (below zero), a heatlamp or heater in the coop is a good idea.

Well, you are looking for a heavy feathered bird that isn't overly excitable and is a good egg-layer--any of the heavies would suit your needs (orpingtons, rocks, wyandottes, cochins, giants, rhode island reds, sex-links (red/black stars), brahmas are a few examples)
To find out more about these and more go to: http://mcmurrayhatchery.com they are a great source for information and poultry. Easy to deal with and pricing is okay. Also they sex their chicks so you can get all hens, roosters, or straight run.

Good Luck and I hope you find some chickens you like.

Oatman

1- I've read in books that one nesting box is needed per every 5 birds. But I think that's a high estimate. Mine tend to fight over boxes and some end up laying other places. So I think 2-3 birds per box.
As for roosts, as long as they each have room to sit, they should be fine. However, like Oatman said, the birds on top (usually the dominant ones) will sometimes get bossier to the others. I make sure all my hens have their space.
2- a 3 feet fence sounds rather low. Ours is 4'. Our hens COULD fly over it still if they wanted to, but our yard is big enough and they're happy that they don't bother to try. (Other hens have done it in the past.)
3- Oatman answered that question really well. If you keep your coop free of drafts and the chickens have each other for warmth, then you'll probably be okay. Then again I grew up watching Little House On the Prarie (isn't that MN?) and boy, your winters can be rough. I reccommend a heat lamp also, on your coldest days.
4- Breeds: There are so many to choose from! Check some catalogs or online sites (such as mcmurrayhatchery.com) to get more detailed information. Some will specifically say "hearty in winter" and things like that.