Your brother's circumstances are not relevant to your application. He cannot help you with an EEA family permit, nor with immigration under the non-EEA route. Your wife will be your sponsor for an EEA family permit, because she is Hungarian.
Immigration under the (non-EEA) immigration rules is not available because you are not your brother's spouse, partner, fiancé, child, or caregiver; see https://www.gov.uk/join-family-in-uk.
Your wife can move to the UK and stay there for some time as a job seeker, but in fact she need not provide any justification for her presence in the UK for the first three months. She has a right under EU law for you to accompany her, and this is the basis for your EEA family permit. See https://www.gov.uk/family-permit/overview.
Because your wife is not yet living in the UK, there is no need for you to answer any questions about employment, finances, or accommodations.
To settle under the EEA regulations, your wife will need to find a job (there are other ways to qualify, but that is the most common), whereafter you can apply for a residence card. See https://www.gov.uk/apply-for-a-uk-residence-card.
You are surely aware that the UK is in the process of leaving the EU. This means that it is very likely that this legal framework will cease to apply, probably in 2019. The options that would be available to you to remain in the UK at that point are uncertain.
Finally, even if your brother were an EEA national, it would be less secure for you to apply under his sponsorship because you would have to qualify as an "extended family member," which is rather more difficult. Also, if he becomes a British citizen, he will be unable to sponsor you under the EEA regulations because that route is not usually available to the family of British citizens; instead, they must apply under the immigration rules.
