If the participation of both spouses is significant (such that it would not be proper for one spouse to claim the activity as a sole proprietorship), then either a partnership return or two separate Schedule C wherein each spouse takes into account his or her respective share of the business items as a sole proprietor will be used.
For more on each spouse using a Schedule C for their portion, please see Husband and Wife Business "The provision generally permits a qualified joint venture whose only members are a husband and wife filing a joint return not to be treated as a partnership for Federal tax purposes."
It may even more accurately reflect the various activities within the business (such as the teaching being reported only by the mom) by using two Schedule C in a joint return.
When filing Schedule C, whether one or two, the efforts of the son would be recognized by paying a wage or salary to the son. The son will not have to pay FICA but will have earned income subject to income tax
See Family Help and links at Businesses with Employees for details.
If the business was actually a three member partnership then a partnership return will be filed (whether or not you formed an LLC). See Partnerships for more details.
Of course, to file a return the partnership will need an Employer ID Number (EIN)
So, you will have to decide whether the activity was a sole proprietorship, a joint activity by spouses reported as two proprietorships or a partnership.
In the first two cases the son would be an employee and in the last a partner.
The start up costs would be deducted by the proprietor, allocated between the spouses or taken by the partnership.
Best wishes on your family business.