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Generally speaking, March is better than January; it will be a bit cooler and you leave the carnival rush behind.
You don't state how long you're going. If it's a short trip (1-2 weeks), staying close to Rio and perhaps making one foray is a good plan. Overland travel is slow, because distances are long. But, a flight to something like Iguazu might be worth it. Or, you could take a bus to Minas Gerais and spend a few days in and around Ouro Preto.
Rio is very photogenic, has good beaches, decent restaurants, and everyone serves a good caipirinha.