Higher interest rates and shorter terms are part of the deal, but they can get you that quick cash you need for the purchase and rehab.Then, there's private money, which might come from individuals like your dad or other investors looking for a solid return.

We here at BiggerPockets have heard for years, even before interest rates went up, that deal finding is a top challenge.   

At what rate is your local RE market appreciating?

I found a property that cash flows around $100-$150 in Bakersfield, depending on the interest rate, but I am wondering if it is a good idea to take this and run with it as a first rental, in order to be able to cash out refi in the future to be able to put a bigger down payment on a mult-family property.

first off if you have to buy a system those are not true private money lenders those are HML ers full stop.private money lenders are folks that you meet personally.. at REIA meetings etc.. other professionals that you may encounter in your day to day that would have invest-able cash. many of these professionals will have IRA solo K profit sharing plans and those are your perfect investor. otherwise quit wasting your time and find the nearest HML that are REAL  ( tons of fakes) their rate will be basically the same as private lenders generally speaking

My first house was expensive , rates were high , it was $51K in 1984 .

You will want homeowners for your side, landlords insurance for the other.One advantage of landlords insurance is that the rates tend to be lower than homeowners rates because you do not insure the contents of the home.

Fayetteville's annual population growth rate is sitting around -0.38% , -0.40% growth since the 2020 Consensus has been recorded.

What rate can I expect? 

Lowest rates to pull cash out are conventional sources, particularly if you owner occupy the house.