The main image on the Earth Prime Batman page looks to be from the New 52 era, that suit isn't used anymore and as such, I suggest updating it with an image of his most recent primary costume. Probably a different image of this suit would be most appropriate.
How is it the most recognizable look ? The most current look, is more classic looking than any Prime Earth Batsuit, it's very iconic looking and is more or less the exact primary costume he had in prior to the new 52. It's not some arbitrary change in appearance either, it's a very different looking costume than the one he had in the start to the new 52. If anything the New 52 costume is the one of the most irrelevant costumes in the history of Batsuits, being such a strong departure from what came before.
Factually speaking it's the essentially the same costume Batman had before the New 52. Dark blue, cloth pouches, no armor, trunks. Discounting the Batman Inc. outfit, it is the latest New Earth Costume, just compare and contrast Jim Lee's design with the current design, it's the same, I can't tell the difference, and perhaps, my choice of words was incorrect, I just always felt that the New 52 suit(s) were sort of a fad and that the Batsuit would always return to it's roots.
No point in arguing semantics, but OK. There is such a thing as a definitive base look, that has existed for over 75 years, that look consists of a blue/grey color scheme, trunks, and a lack of armor. Things such as ear length, look of the utility belt, and bat symbol have all changed over time, those have not, and my point has been proven time and time again outfits, that don't incorporate core aspects are fads, they always have been, and always will be. Suits like the Troika suit, Batman Inc suit or the New 52 suit come and go. I recommend reading older comics along with the new stuff, it would change your perspective.
Prime Earth. But it’s not one timeline, and the overall differences are too big to say they’re one.
If we’re getting a new image, it has to be, preferably, a textless cover by someone who has also done interiors for a considerable tenure. For this version, that probably makes Capullo the prime candidate
It could be anybody, I've never been the biggest fan of Greg Capullo's artwork as it looks so different from any other artist, but I understand his appeal. But I do agree, it would have to be artwork by somebody that has been going at it for a while.