Yes, you can change costume any time.
Noir costume is great, but when you first select it, you'll be asked within the costume menu if you want to enable the black and white filter. There's no separate place to enable or disable it so you need to do it from within the costume menu.
Also if you fancy the old 98 sound track (which amazingly also changes all the sound effects to the one's from the original RE2) that is found under the Sound settings inside the options menu.
I would still recommend play with the defaults first, because the defaults go through wear/tear and natural changes (like bandages and shit based on events) that aren't reflected on the alternate costumes.
Finally, once you beat a game, the story menu will have a new [2ND RUN] entry, you wanna play that for the second half of the story.
eg if you start as Leon, you should play Claire [2ND RUN] to see the story from Claire's POV for Leon's events.