The first thing you need to do is decide how you're going to set up your business. You can be partners in the legal sense of the word and still be a sole proprietorship. A sole proprietorship means exactly that -- a "sole" proprietor.
If you are both working together in a business, the fact that you've even said, "Let's be partners," makes you a general partnership until you do something different. You don't want that as you are as liable for the actions of your general partner as much as you are your own.
Bottom line, you need to form an entity, either an LLC or a corporation. Talk to a good CPA to find out what is best for you.
As for borrowing, you're right...with no assets, most banks are not going to look favorably upon this request. However, if your father could qualify for a loan for the $300,000, then the bank could make the loan to your business with your father as the guarantor. Having said that, if the bank does not think that you can make a go of your salon business, then they are likely to just ask that the loan be made directly to your father, and then he can, in turn, invest the money in your business.
A bank will not make a loan to a business knowing that there's a poor chance of repayment without a guarantor, and they don't want to go through the legal process of using the guaranty when they can just have your father on the hook personally from the beginning.
$300,000 sounds like an awful lot of money for this venture. Are you sure you can't just find an existing business and buy that instead? Also, is this really the best time economy-wise to start this kind of service? I could see buying one cheap that has fallen on hard times and then wait for the turnaround, but I can't see starting this business from scratch today, unless you are working with a very upscale neighborhood that has little competition.
Are you really prepared to actually run a business? It all sounds so easy, but it's very, very hard. I would seek out a mentor, if possible. Do you have a local university with an entrepreneurship program? How about a SCORE office?
I wish you well.
