I stayed at a B&B in Ipanema via Airbnb and loved it. After walking around Copacabana and other parts of the city, I was glad I chose Ipanema - the beach was great, there are lots of great food options and it felt very safe. It's a pretty intense place, however, because of the sheer mass of people and 24/7 vitality.
I loved the city's buses. From Ipanema, it's easy to catch a direct bus to either Corcovado or Sugar Loaf, or just about anywhere else for that matter.
Tip - It can be tough to flag down your bus because it can be at the back of a long line of buses that pulls up at same time. And before you know it, your bus can pull around the others and take off. Just be ready to wave like a madman.
There's lots of information about the airport buses in other threads, so all I have to add is that it's ridiculously stupid how difficult it is to get your luggage onto these buses. It's as if they were designed explicitly to not allow any luggage onboard.
If you do stay in Ipanema, don't miss watching a sunset from atop the rocks at the east end of the beach. Quite the nightly event.