I think Reeves is going to have a sprinkle of 'burton' to his batman, in the same way he'll be treading into the mind with this - why is a man dressed as a bat? why does he do it, what is it all for and therefore i think he'll play up the craziness to do it/pull it off.
Bruce will literally want to hide away in this world he has created due to ptsd and it will let him be this different person and use theatrics to get his point of view across the criminals.. i think to begin with, that will be his motives then as he gets more experienced, the suit will be tweaked and more secure. I can see the cowl looking organic, i can also see this batman looking the most 'evil', like a gargoyle - i even think that will be part of his stealth to blend in, up on the roof tops.
See, if that were the case I would pretty much lose a lot of faith in Reeves' vision straight away. All black rubber is a possibility I guess, and I wouldn't mind that personally-- but I would be very surprised if he's just going to immediately revert back to another Tank and a stripped down realism approach to the whole world. I am trusting that he's smart enough to know that just following Nolan's approach while making it more of a noir detective story isn't going to be enough to give the franchise the breath of fresh air it needs. And with this film supposedly being packed with villains, I see that lending itself to a more fantasy-based approach.
It just seems like it would lack imagination if his vision for the universe is an extension of the Nolanverse aesthetically.
I think the car will be a side project thing, he will use a bike to get around - a car stands out too much but i think, for one instance, he uses the car... and it's more used as a distraction, speed... than protection - he won't be hanging about. no pun intended.
It's like wayne mannor has a garage for old cars, concept cars etc and bruce takes a shining to one, devilish look drag racing car, the plot requires him to get to arkham/gotham in record speed and knowing the underground routes, paths etc, that's the best thing to use.