You dont really need a whole lot of money to start a business if your business is a service business rather than one in which you need to carry inventory but you'll need SOME money for a business license, taxes, and advertising. The business you decide on should be one which uses your time...
The problem with naming a business after a person is your reputation is still on the line after selling a business. I would discourage your Dad from using his name in the business name. Pathways to Success may be a better choice.
There are a number of programs and resources for help but your bad credit might hinder you. Financers and investors are more cautious of risk than ever but that doesn't mean it's impossible. You really need a business plan to prove to yourself and your creditor(s) that you can reach a break even...