What kind of lender do I need? Self-employed, small loan amount

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I am looking at a piece of property that will cost about $65K. I can put down $30K but would like to borrow the rest. This will be my first real estate purchase and my first loan. I am unsure what kind of loan I should get or for what kind I might qualify. A conventional mortgage? A large personal loan? A private lender or hard money?  I am still learning the basics about loan options.

I have very good credit (650-700) and no recurring debt payments, but I am self-employed. I didn't earn enough to file taxes in 2015 so I have no tax returns from last year or W-2's to provide. I do have current bank statements that show regular deposits of $5K/month. I don't want to wait until 2017 when I have 2016's tax returns available, as I would like to buy the property now.

I would think that with a high credit score and such a large down payment, I could get some kind of loan, even if at a higher rate and with shorter terms -- but I am new to this and don't know where to start.

Other details: I live in California but am buying property in New York. The property is an older home, built in 1880, which needs some finishing -- so it might not meet all the requirements for a traditional mortgage loan.

Where should I begin?  Do I need a mortgage broker?  A loan officer? 

All advice is much appreciated.  I'm not seeking recommendation for a particular lender, please, just the kind of loan most appropriate to my situation.  Thank you!