I'm looking to purchase my own property and want to use the money from the sale of the property for my next home but all the equity is under the business name. 

This could be an individual person willing to give you money, or a private bank, or an organization or business of some sort.The long answer is much longer and if you're interested in diving into the topic here's a few resources I can recommend:These are two great books (also available as audio books and e-books) that go over the fundamentals of what private lending are, what it means to raise capital, how to find deals to buy with private capital, and a lot more.

My name is Brittney, my husband and I are in the process of starting our own fix and flip investment but unsure how to proceed and get our first investor, preferable a private money lender because we dont have the capital, or credit to get a loan and you have to wait at least 6 months after opening an LLC and getting a business line of credit in order to apply for a loan.

I find that's definitely the first thing that is good to think about, you'll hear people talk about their "buy box" which is just a way of saying what kinds of deals and opportunities you're interested in. 

A lot of people are afraid to learn these skills!

Any thoughts on whether this should be borrowed as a 'homeowner' or 'business'?

This business is heavily based on relationships, so in most cases, the referral you get will be highly biased by the relationship between the realtor/lender and not necessarily what's most objectively reasonable.

However, this approach may require a compelling story or project to attract contributions.Some people opt for personal loans to cover the down payment, though this can come with high interest rates.Lastly, some private lenders may base your loan amount on the property's as-is value rather than the purchase price.

That’s what they are afraid people would do. 

It is great to introduce myself to like minded people.