Great questions @Eric Harnden. I'd wholly support house hacking as your first venture.
During my first year in the property, it helped me to picture my expenses as being the same as if I were renting, except now I had a bonus $525 income stream that I could put into savings each month. I never considered the duplex as cash flowing anything while I lived there because my mortgage was $900+ and the tenant was paying $525. Now that I've moved out, the combined rent of both units covers the mortgage, 10% capex put away, 10% repairs put away, water payment, and leaves just over $100 as legitimate free cash flow.
Treating my duplex mortgage as the same as my prior rent expense kept my weekly and monthly budget close to what it had always been, except every month I'd see this magic cash that was coming from the tenant stacking up in another bank account. I also deposited the rent into a different bank than my usual and shredded the debit card so I couldn't spend the money except with great effort. A year later when I went to update the tenant's kitchen, I had about $6000 sitting in savings that I used to pay for the repairs.
Thus, I considered the tenant's rent as an extra savings or bonus income stream that I wouldn't have if I were renting or living in a single family home. For the first year, I paid the mortgage out of my usual earnings and saved her rent which I then re-invested in the house by renovating the kitchen and, later, doing the other repairs I laid out in the post. There were a couple of months where I was changing jobs and during those months I would directly apply my tenant's rent to the mortgage versus saving it.
The $20,000 was the combined down payment, closing costs, and capex/repairs expenditures over the three years that I lived there. Total capex for repairs, renovation, paint, etc. was approximately $13,000 while the other $7,000 was my initial down payment and closing costs for the loan.
This duplex allowed me to save enough capital to be able to buy other rental properties cash from the auction, take care of all repairs up front, refinance and collect cash flow within the first 3-4 months after purchase.
Let me know if that clears things up. I'm not an accountant so there may be a clearer way to segregate or explain the income/expenses than the way I did.
Best of luck with the house hack or whatever you choose to do.