The Rebellion was started by dignitaries, namely Mon Mothma and Bail Organa, they were not exactly poor from the get-go.
Mon Mothma was born in 48 BBY into a wealthy and influential family
living on Chandrila.
And as I remember from reading the X-wing series, the forming of the Rebellion is mentioned, and her name is mention as the one who will supply the star fighters for the Rebellion I have forgotten which exact book it was and hence do not have a quote, however I found a blurb about it on the wiki:
During the early days of the Rebellion , Mothma took a leadership role in many important missions. These included gaining the X-wing starfighter for the Alliance and finding the plans for the first Death Star. Captain Raymus Antilles acted as her right hand man until his death.
(Both above exerts from http://starwars.wikia.com/wiki/Mon_Mothma)
Bail Prestor Organa
Bail was not born into wealth as Mothma was, however he did create a career in the senate for himself. He became ambassador for Alderaan, and later went on to marry the Queen Breha Organa, making him king and part of the royal family, and therefore ruler of Alderaan. He therefore had large sums of money, and even military, at his disposal.
(See here for more info on Bail)
I also recall other people being mentioned in the X-wing novel (MonMothma for the starships, another man for the soldiers if I remember correctly...), if only I could remember which one it was and get a specific quote. If my memory returns I will edit this answer accordinly, but for now I think there is still sufficient evidence to support the fact that the Rebellion was created by people with great wealth, and could therefore afford to confront the Empire.