Foremost, you should probably start the process as soon as you can. Even if you arrive in Canada before filing the PR application, still file what is referred to as an outland, or outside of Canada application (yes, a person can and ordinarily should file the out-of-Canada app even if they are living in or temporarily located in Canada).
Begin to familiarize yourself with the process, the forms, and so on, at:
http://www.cic.gc.ca/english/index.asp
Application forms, checklists, and guides for out of Canada family class are at:
http://www.cic.gc.ca/english/information...ons/fc.asp
General timelines for sponsored partner PR applications at posted at the CIC website:
http://www.cic.gc.ca/english/information...pouses.asp
"Can" you move between the U.S. and Canada? Sure, if you have status to do so. But, generally, both the U.S. and Canada are entirely independent sovereign countries, each independently controlling their own immigration. A foreign national cannot "move" to either country without proper status to do so. Status in Canada really has little bearing on what the U.S. allows (recognizing though that Canadians and Irish passport holders are both, generally, visa-exempt, meaning they can visit the U.S. without having to apply for and obtain a visitor's visa in advance), and similarly, status in the U.S. has little or no bearing on whether a person can move (or even work) in Canada.
The fees to apply for PR for an individual (I am assuming that by "Canadian" you mean your spouse is a Canadian citizen, thus your children are Canadian citizens and do not need to be included in the sponsorship; if for some reason the children are not citizens, its another $150 each):
application fee: $75
fee for PR applicant: $475
Right of PR fee: $490
("landing fee")
Total fees: $1040
There are, however, various other costs, ranging from obtaining the necessary certified copies of certain documents if you do not already have them, costs associated with obtaining items like the police certificates (such as fingerprint costs if applicable), photocopying costs, and courier service costs (it is wise to do everything by courier even though that costs significantly more than ordinary mail).
You will not be allowed to work until you actually land as a PR. Note, some are tempted by the fact that inland applicants who obtain AIP (approval in principle) may obtain an open work permit pending the final determination of their application; however, the minimum time to obtain AIP for inland apps is almost always at least as long, or close thereto, as it takes for the vast majority of well-qualified applicants who submit carefully and thoroughly completed out-of-Canada application, but it can be much longer,
so there is usually no advantage to the inland process in this regard.
Once a PR, you can definitely bank in Canada like anyone else in Canada.
Non-resident visitors to Canada usually can find a bank at which they can have at least a joint account with a Canadian. Many report having problems being able to open their own account, and some report problems even opening a joint account, so it may take some bank or even bank branch shopping to find one. I opened a bank account in Canada many years prior to even thinking about coming to Canada as anything other than a visitor, but I think things have changed since then.
Should note that relative to working, actually there are some U.S./Canadian provisions relative to trade agreements that have bearing on working on the "other side of the border" but they would have no application to you in any near future scenario.