The Sheraton Barra opened 2 years ago - great property, all rooms have a nice balcony with beach view. The "other" Sheraton in Rio is backed up against the favela, and there is nothing else but favela for several blocks, making even the smallest trip out of a the hotel a bit of a nuisance, and a long walk or short taxi ride to ANYWHERE.

Regarding a copy of your passport, best bet is to take a color copy of your photo / signature pages together, as well as a copy of the page that has your visa, and one more of your page with the entry stamp for good measure. If you do encounter police that want to go so far as to question if you have your passport, (almost always Military Police who are just looking for a few $R) - then this will show that you're prepared and be more than what is required. Many times tourists who do have a copy of the photo/signature page are questioned as to if they are beyond their visa stay, having the above 3 pages would quickly end this line of questioning.

However, on the road between Barra and Copa, if stopped by police, usually just stating that your a tourist on vacation (in English!) will get you waved on.

*Edited to add the following*
As the original poster was asking about apartment vs. hotel - if it is your first visit, I would definitely recommend that you stay in a hotel. The location really should be based on what type of vacation you're here for. Relax / beach / watersports can be great in Barra, with some nightlife. More on the side of nightlife and clubs, Ipanema. As for Copa, well Copa is Copa......