If we're going with a new Superman approach - and something slightly more believable, like Nolan's Batman films - then nanotechnology is the only way to go. I just can't see today's audience accepting the old phonebooth costume change, not with the kinds of crowds we have on the street nowadays 24/7. It's fine doing a superspeed change, but someone will see him entering or leaving. And if he does that at superspeed, then what's the point of going into the phone booth?
I'd like a film where Kal El basically puts on a Kryptonian uniform of some kind as he starts out in his role as Superman. And the entire uniform is generated by nanotechnology. It can switch almost instantly from it's default look to his Clark Kent suit/shirt/tie - and again to the Superman costume.
No need to wear clothes over the suit, no need to carry it with him, and no far fetched explanation needed for where he hides the boots and cape. The suit is on him at all times - but he can change how it looks whenever he needs to.
A lot of the comics had the Fortress not as an ice palace like Donner's, but a futuristic building populated by robot servants who monitored Superman's vital signs, etc. I always thought a nano-suit was the perfect way to implement this, it can be used to monitor him while he wears it and even enhance his absorption of solar power. Perhaps it even has enhancements which make it easier for him to engage in deep space travel, etc.
Let's not forget, Superman comes from an advanced alien civilisation. Even referring to the Donner universe, they had enough power to accomplish deep space travel and use a single crystal to build a fortress structure. I don't think it's a huge stretch of the imagination to assume that nanotechnology would have been part of their science, given that we humans are already aware of nanotechnology and researching it - and we're way, way behind Kryptonian technology.