Why not start with a guide book, such as the Lonely Planet guide to Brazil or any of numerous others? Eaiser for you to see a wide variety of places and decide what appeals to you. I wouldn't let a local tour operator determine my whole itinerary for me, and I speak Portuguese. Brazil is the size of the continental U.S. You mention 10 days in Brazil but address only Rio. A guide book, and a look at airline costs and schedules will help you determine just what you want to, and can, see. You can always find organized tours for specific locations, such as the city of Rio. If you want your entire stay organized in advance, I think you'd be better off dealing wiht a U.S.-based operator, especially if you don't speak Portuguese and don't wan to be with a group tour, without English, for your stay. When my mother and a friend visited Brazil, while I was working in Rio, a U.S. travel agent arranged flights and also semi-escorted tour arrangements in each city.
Important: by "winter" I assume you mean the Northern Hemisphere winter. If you will traveling over New Years and/or Carnaval, you will run into higher than usual costs, minimum stay requirements (especially in Rio), etc. and may be too late to arrange hotels except at super high prices (if at all). I would agree with the above poster that you should try to get out of Rio itself. World's most beautiful city? Very subjective (others would vote for Hong Kong, San Francisco, Paris and others-- some of which may be be cleaner and more modern and safer, but without the nice beaches, found in or near Rio). And I'd still try to see a variety of places, depending on what your interests are (which you don't indicate; another reason for a guide book). Foz de Iguaçu, Ouro Preto, Salvador, Pantanal, Amazon jungle all worth considering. No way you could see all of them, plus Rio, in 10 days. And the itinerary that might be good for me may not suit you. Start reading. And start looking at flight and hotel costs.
BTW, even when I lived and worked in Rio in the mid-90s, and lived in Ipanema, I seldom went swimming there, due to the pollution. Many others did, and even without swimming the scenery was great-- both human and otherwise. Barra de Tijuca, on the northern outskirts, has some nice beaches. And keep in mind that Brazil is not a cheap place to visit, even when the dollar is strong. It's not like visiting Argentina or Mexico.