I believe a 203k loan would allow you to check all of your boxes. A 203k loan is an FHA loan, with an FHA sized down payment, that includes the cost of major repairs in the mortgage.

The 203k program is similar to the Healthy Neighborhoods program except it is a federal program and applies anywhere.

How it works, generally speaking, is you find a house that wouldn't qualify for conventional financing because of at least 1 major problem. For example, you find a house but it needs a new HVAC system and windows. The 203k loan will include money for those repairs and any other repairs needed to bring the house into code compliance.

The money for the repairs is held in escrow until each job is finished. This eliminates expensive financing since the repairs are part of your mortgage.

This would eliminate your getting a crappy flip and widen the pool of potential houses.

Plus, the cosmetics would be up to you so you can make your new house into your home.

On a side note, I noticed someone had mentioned the problem of sewage backing up into basements in the city. It is a lot easier, and maybe cheaper, to be proactive and prevent a backup, than to clean one up if you have to hire a company to do it. The fix involves installing a back check valve in your sewer line. I believe they can be installed on your main sewer line but are mainly installed on pipes connected to toilets, laundry tubs etc. in the basement.

Happy hunting and good luck!