I am looking for some information on a new patio. Area is 12x40 and will be intalled around a deck and some landscaping so a little more complicated than a simple slab. First question is cost, what are the comparisons on cement, stone, pavers. Then, because I live in Michigan (some years we get a lot of snow, varying temps) is there one material better than the other? Thanks

No pictures, no idea on what type stones you would plan on using.
Up to you to take the measurements and do the math on differant material.
Not sure how anyone here would know the price of materails in your area.
Do you plan on doing the work yourself?

i am also a resident of MI, if your going to do it yourself take a good look at pavers. stamped concrete is a good patio option. either will work good as long as it is installed properly. if you go with pavers make sure to compact as you add fill this is key to having a patio stay stable thru the winters. as far as pricing, get some quotes most contracters will be happy to quote the stamped concrete. any of the landscaping supply outfits will give you cost of materials after you pick out pavers