CarnAval

Well, first of all, Carnaval is a party, a wild party in many places, traditionally to celebrate the coming of the deprivations of Lent, so to expect a quiet time is not realistic.
"Best" is completely subjective.
My jaded feeling is that most foreigners come to Carnaval to stay drunk and easily pick up s** partners, and where they do it is a secondary consideration.
Forget "affordable". Forget" not too crowded".

The three major Carnavals in Brazil are Rio, Salvador, and Recife/Olinda.

Rio:
Rio has the big hotly contested competition among the 12 top (neighborhood) samba schools held in the Sambadromo on the Sunday and Monday night of Carnaval week. There is a yearly theme for costumes, floats and songs, and each school does its own take. Lower level samba schools compete on other nights, and there is a reprise of the winners of the top schools on the Saturday. These are ticketed, at varying cost. Neighborhoods prepare for the competition all year. Rehearsals are usually open to visit.
There are also street parties (blocos) in most neighborhoods. These are free.
A link to the list of blocos and rehearsals is now posted on Lonely Planet's Thorn Tree forum for Brazil.
There are also some ticketed "balls" around town.
Usually hotels are filled to capacity at highly raised prices for multi-day packages. Lines at tourist sights are long and beaches crowded.

Salvador:
Salvador's Carnaval is about its unique local music styles, bands and singers. All are nationally famous. There are two main routes, in the city center and along the seaside, along which tall semi trucks carry the bands and singers, all afternoon and into the small hours of the morning, every day of Carnaval. There is also a route in the historic district. Partying goes on all over town, all night, every night. You can buy entry to one of the viewing stands, with food and drink usually included, you can buy an abada, a T-shirt that allows you to dance along the route in an area behind a band you like protected a bit in a roped off area, or you can "go pipoca" , like popcorn, jumping in the general crowds on the street. Salvador receives at least a million domestic and foreign visitors for Carnaval.

Olinda:
Olinda's Carnaval is famous for its huge puppets who dance in the parade. This Colonial suburb of Recife, as well as a Recife itself, has partying in the street.

There are other smaller towns, like Ouro Preto, that are known for their Carnavals.
All beach areas are crowded with Brazilians who just want to get away to the seaside.
Most all accomodations at most all destinations sell higher priced multi-night packages for Carnaval.

Hope that answers some of your questions.