Travel through the "Grande" Brazil on a budget is a hard work. Before going, look for your way out of the country, because a lot of your budget can depend on it. The cheapest is probably by land, if it is on your plan. To fly out is the cheapest from Manaus in the Amazon, specially up to Miami, the way a lot of locals go. (The Brazilians are the 2nd biggest shopping people in Florida after the Japanese). If you go that way, Surename Airways have cheap flights from Fortaleza, in the north.
Having said that, first the transport, the one who will make a Big dent in your budget. Check flights, because a flight booked a week or more ahead will sometimes be cheaper or equal, (safer also, considering the Brazil bad reputation on security) than your bus ride. Look for bigger cities closed to your destination for flight sale, and different companies, depending of your destination.
Second, when you stay longer in one place, you save by not paying transport, you can deal a long stay with your hotel, and you have time to find the economic places to eat. For your hotel, if you mention that you can pay cash, they can give you a lower price. But before all that, shop around or shop on line, because you have all kinds of possibilities, and remember that many times you can only get for what you pay, but not all the time if you are a good shopper. Some towns have more economic places to stay, like the beautiful Praia de Pipa, near Natal, to mention one. Or if you can be ready to walk a little, staying at 10 or15 minutes walk from the center, or a bus ride. If the city you want to see has only expensive hotels, do it in a day trip. Example, you want to see Arrail d'Ajuda (A ferry across is R$4 for tourist) and its beaches , or the colonial Trancoso (50 minutes by bus near the ferry terminal), stay at Porto Seguro for half the price with breakfast, and more choices for dinner.
For the price sometime, and for your comfort, travel by two so you can have a private room. Shared bathroom can be cheaper but most of the time you have ensuite rooms in Brazil. There is big dorms sometime in Brazil (you can see dorms of 40 for Rio..???). Do more research you can find better, look for 4 or 6 and with inside bathroom if possible, you will have a better travel and make it for your budget. There is exception in some cities. (Salvador is one)
Walking is another economic way if you can avoid the expensive taxi. Brazil also has a good city bus service most of the time, even from the airport. Some cities, have metro (example Recife) The price ranges from US$1.00 to US$2.00 even in Rio. With patience (specially during rush hour) you can go almost anywhere.
Your next expance: food. If you choose a hostel, choose with a kitchen or breakfast included. If not you have the "per kilo restaurants" but shop around, they can range from R$12. To R$40 a kilo. For more economic is to find where they make you a plate from the buffet for R$7 to R$12/. If you can find it there is also the business plate make for workers. It can starts from R$5. But remember, it might not be the home taste or having no taste at all. If you like beer! In store you will find the cheapest one, Skoll is the most populor. For fast food, you have all kind, even US$25.00 for a plate. Look around for the small ones and reasonable ones.
Bring more than one banks ATM card, bring cash or travelling checks if you like them. Brazil has Bank ATM issues (Bradesco and Banco de Brazil are the most popular). They don't take your card or they don't work internationally for sometime a week. Keep that in mind, also when you will go country side.
Finally, when arriving in a Big city, looking for a hotel, remember this: Near a big hotel there is always an economic one. (principle of business) .