Very new here, but have done a lot of reading around here.
I read somewhere around here that the 1'x1' stick down linoleum isn't that great because the sand and grit and junk starts to work it's way under and the corners start to peel up and then the chickens start to peck and pull at the corners. I help do repairs on my parents rental properties, and in my experience these stick down squares usually aren't worth it.
If you were to do the deep litter method, this might not be an issue, but with sand and stuff, i think it could be.
Another option would be to buy linoleum off the roll at a local store (like Home Depot). The cons to this is it is supposed to be glued down, and that can be a pain.
If it were my coop (the ones I manage are all concrete floors), I'd get whichever was cheapest by the square foot, and nail/tack, staple the suckers down. If the price difference is not that much, I'd go with the single sheet as it would use less nails. Just use small trim boards/firring strips/whatever you can find around the walls and nail down through them through the linoleum.
As you have a coop you can't walk into, I am assuming the area isn't that big, so you would probably be better off using the stick down stuff. I'd slap a small headed nail (not a finishing nail and not a huge nail either) in each corner, and you would proably never have problems (but if any started to come up, just replace it if it's too bad, or just nail that part).
Then again, I am new here and just remember the one post about those stick down types. Other people may have had great success with them. Good news is you should have a lot of good advice pretty quickly.