Since filing for immigration seems a bit much for a visit of no more than a year, you might consider some temporary options.
Your wife and children could seek a 1-year admission in B-2 status ("visitor for pleasure"). The usual period of admission is six months, but the regulations permit admission for up to a year. If I recall correctly, one case in which this is done is long-term family visits. You would probably need to show good evidence that you plan to leave at the end of the year, because the visa officer and the immigration officer are required to presume that your wife and children intend to immigrate, and the applicant must overcome that presumption to qualify for B-2 status.
If you limit the visit to six months, it will probably be that much easier to overcome the presumption of immigrant intent.
It seems that there may be some trouble for your children attending school while they're in B-2 status. Officially, they are not supposed to do that if the primary purpose of the trip is to attend school in the US, but they can do it if the study is incidental to another purpose (such as accompanying you). Your children who are in high school or above may therefore want to apply for an F-1 student visa instead (younger students cannot qualify for an F-1 visa).
If obtaining US citizenship for your children is valuable to you, but you definitely won't be staying for longer than six months or a year, you could apply for your children to immigrate while pursuing the nonimmigrant route for your wife. Your children would becme US citizens on arrival as explained in user102008's answer. This approach, however, might make it more difficult for your wife to overcome the presumption of immigrant intent: why are the children applying for immigration when she is not?
In any event, it is probably worthwhile to look for a good US immigration lawyer. The simplest route here is to apply for immigration for everyone, and many people prefer to hire a lawyer even for uncomplicated immigration cases.