These are all very beautiful prints - and I'm inclined to say that the one in pic #1 has the most likely chance of being supportive, *if* you add a halter strap or straps of some kind. I'm not as crazy about the tank style you linked to, although I can see how it would be a bit better in terms of support - just that this style doesn't look as nice (to my eye) as the others.
Is it possible to get something like the one in #1 and have a tailor put a halter strap on it? Wide straps, not like the super thin ones in link #2.
I think you could easily order something from this list, but that you'd want to take the suit to a tailor and have a wider (halter or otherwise) strap(s) attached. I'm willing to bet you can have any kind of strap(s) attached to these - you might end up buying some material from a fabric shop (bathing suit material in a similar colour to the prints) and then taking it to your tailor.
I can't imagine why the following types of straps couldn't be added to any of the suits you linked to:
halter style:
http://www.landsend.com/pp/wom.....038;sku_0=::RPU&CM_MERCH=IDX_swimwear-_-women-_-shop-by-silhouette-_-one-piece-swimsuits&origin=index
straps attached to suit:
http://www.landsend.com/pp/wom.....038;sku_0=::GC2&CM_MERCH=IDX_swimwear-_-women-_-shop-by-silhouette-_-one-piece-swimsuits&origin=index
Why couldn't you attach brown straps to the "We Are Handsome" one piece with the lion print? You could also remove the teensy-tiny straps in the ruffled blue suit and attach some straps or a strap that was a bit more substantial.
Yes, a hassle - but if you love these prints, I bet it can be done relatively easily.