I suppose if I wanted to move into the modern age I would probably use QuickBooks by Intuit. 

This is what everybody else is doing already, including Intuit.- "At the end of the day... customers were craving a person, rather than a computer to do their accounting."

I need something that is intuitive, pretty comprehensive, and not too expensive (don’t want to break the bank with this as it’s my first investment property).

I don't always trust my intuition on these things if it's not my area of expertise.

My intuition is to go with the family that lives in the area already and has looked at the home but since they are willing to pay more in rent, I'm not sure if that is an ethical decision.

I'm not too familiar with Quicken, but it's a trademark of Intuit.

Further, the explanation of if you only receive your profit a little at a time you’ll be able to “find” deductions to offset it is counter intuitive- either you have deductions from income or you don’t - you don’t “find “ them .

Do whatever your intuition tells you to do but the deal is where its at.

That is not intuitive!

Some numbers can be deceiving or counter intuitive.