I'm a huge tech head but I also agree we shouldn't get hung up on the details - I'm just as interested that what could be a Patton-esque war film would also have a kickass story that these kickass designs and animation and costumes will support.
That said, the Ares is fantastic, and using the Kelvin should be just fine - potentially being an older water horse in the Four Years War, large and slow fodder for nimbler Klingon ships. The other JJ designs may give too much of an impression that this is the JJverse, so I would suggest that they be used sparingly and heavily mixed with other prime-esque designs.
So, unless it's a spoiler, would we be seeing actual representatives of the Axanar species? I would think this film would be less exploration-oriented, but the species seemed worth a look at after its appearance in ENT.