I am not sure what price range you are looking for, but neighborhoods like Nicholtown and Morning Side are good options.

With an FHA loan you will need a minimum 3.5% down and closing costs typically fall within the 3-5% range. 

With a $150k FMV, you're starting to get into the range where SFRs are hard to make work.

If where I live had cheap houses in the 50k range then it would be a no brainer for me, but I live in CA where scaling wide to start is impossible because properties are so expense (1-2% rule aint happening here) so I have to make some hard decisions about what my goals are for getting started.I wish there were some general guidelines that work for all newcomers, such as invest local with a single family home and learn about fixing it up and being a property manager (conservative approach), which seems to be the only choice for some people.

Anything in the 1.4%+ range are total crap and I don't want them.The advantages with apartments are you concentrate capital, you can increase value by boosting rents and decreasing expenses, and if you get above a certain price point you can get non-recourse financing. 

However, with the house being 3 BR, it would be outside of her price range.

My estimates on income for the last house I analyzed ranged from $13k - $40k per year.

Buy a rental property upstate since there’s nothing in my price range If i go any lower in my desired Long Island areas?

It may be hard to get good flooring at the cost at the lower end of your range, same with roofs if you are removing the old shingles and putting on a lifetime roof. 

I did search on zillow for recently sold houses at a below market range.