I am not sure how to make the initial purchase...If I use a private loan? 

Unless you are an experienced builder, securing a bank loan can be difficult, and hard money loans often have high interest rates, which can become costly if your project faces delays.

My main dilemma is on financing my first investment property, as I do not have the funding to pay 20-25% down on a loan for investment.

Make sure you're working with a reputable business and double check they have insurance.

Fred Rewey and Tracy Z. have a great course on performing loans and who i would recommend for performing.

If you're considering a DSCR loan, most lenders won't assess the property's value using a cap rate.

Prop tax's some of the lowest the country very low insurance stucco houses tile roofs and desert landscaping all lead to ease of maintenance over time compared to FLA which of course has all sorts of weather related issues that is detrimental to houses .. high prop tax and sky high insurance ( certain areas) But its also growing.. so there is that.

Especially when it comes to annual property taxes and annual landlord insurance policies. 

I don't think I qualify for any conventional or FHA loans as I don't have long enough income history.

Weird, I've never heard of a loan fee being charged (besides appraisal) if the loan doesn't close.