The first day of a week will be determined by culture. It's normally Monday, but I understand that some Christians use Sunday. Followers of other superstitions may use other days for all I know.
Deciding what is the first week of a month is not easy. Consider May 2013, for example, which began on a Wednesday. That's the week that began on Monday the 29th of April. Or consider June 2013, which began on a Saturday, that being in the week that began on Mon 27 May. Most people would say that the first week of May began on the 29th of April, but that the first week of June began on Mon 3 Jun.
ISO 8601 is normally the fount of all wisdom, but in this case isn't particularly helpful as it only defines the first week of a *year*, not of a month - the first week of a year begins on the Monday between Dec 29 and Jan 4, which is the same as saying that it is the one that contains fhe first Thursday of the year. You could adopt that rule for months, but should expect people to disagree with you!