You could do any of the options that you mention, it's just a matter of doing them correctly. $$. If you do a slab, stamped or not, and you back yard is a little swampy, the contractor would want to dig deeper than usuall to give the slab a proper base. This would depend on how deep the soft earth goes. That of course costs more money, but you could do a slab that size, with a few joints cut in it, without the worry of cracking, if done correctly. If the water is more serious than I picture, you might have to do a dry well to get the water away.
If you would go with a deck. I would be absolutely sure that all of you support post aren't pressure treated wood directly into the ground. I would request to the contractor that you want sonotube down to below your frost line filled with concrete to 4"above finished ground level. They can then attach the support post to the top of the concrete with a bracket. Then you won't have to worry about post rot.
I just replaced my deck 3 years ago. The old deck was 10 years old. The pressure treated post that were originally installed were COMPLETELY rotted. I have a damp yard also. Off of my elevated wood deck, it's 5 steps down to a 12 ×22 concrete patio. 3 years old, no cracks. I have about 12" of different materials as a base under the concrete.
Hope this helps.