It is fundamentally a security organization, so the basis for membership on it should be due to either military power (although I don't know how you'd measure it - the top ten spenders?) or economic power, or an index made of both.

India in that context makes sense, and to an extent Japan does as well along with Germany (not because Germany has a big military, but it is a big economy, and Japan spends a lot both on its military and has a big economy). Brazil has neither, with no worldwide force projection, and Nigeria especially does not.

Although I do think there is an argument to be made for India to be on the council and at least one of the Central or South American countries, but I don't think expanding the security council will fix what is broken with the UN.

With regard to the security council--do away with it. Sarko is right that it is anachronistic, but expansion ain't gonna help. The UN needs full-scale institutional changes.