If you start doing business in the U.S. without forming a U.S. business entity and it is continuous, eventually your Canadian company will be taxed in the U.S. under what is called "Engaged in a Trade or Business" in the U.S. and "Effectively Connected Income" to that trade or business. You can form a U.S. entity that is a separate company from the Canadian company if you want to keep your financials separate. This won't help tax wise but will keep the financials straighter and limit your liability in the U.S. more clearly. If you go this route, you'll need an office address for the U.S. company. What kind of company you would set up is highly dependent on your situation and other factors.
If you work for an American employer, then your personal taxes are withheld by the employer and paid to the U.S. government. If you are the owner, the remainder would pass to you but since you are a non-resident there are other special withholding obligations by the U.S. company to you as a Non-resident shareholder. This will be important if you want to work for the U.S. business as all non-residents of the U.S. must have work authorization to work in the U.S. prior to becoming an employee for a U.S. corporation, even one that they own personally.
Note: This is not legal advice and does not create an attorney-client relationship.