Good cash on cash returns take some work, like raising rent over time, doing light value adds, etc..If you jump in and insist on high cash on cash returns from day one you may find yourself in a tough neighborhood.  

Can I immediately change rules/rents? 

Rented home for $1800 per month before selling it.

I currently live in/own a property that would fairly easily split into two units (upstairs and downstairs), and is located in an historic area close to hospitals, restaurants and amenities. 

They typically involve two agreements: a lease agreement that outlines the terms of the lease (rent, responsibilities, etc.) and an option agreement that grants the tenant the right (but not the obligation) to purchase the property within a specified period at a predetermined price.Negotiation Power: Lease options can be attractive to tenants who may want to secure a property for their business while potentially benefiting from any appreciation in property value.

If so, you could consider renting by the room to increase your gross monthly rent.

My wife and I have been also mulling the idea of when we build the duplex of living in one and renting out the other while we sell our home we are currently in as well and build our dream home.

How would I analyze a deal in a market where the rents are capitulating and is unsure how much or how long it will continue to do so?

Also, what can be rented out easily, in terms of size and number of bedrooms?

I just picked up a Duplex ALL IN, 75k, rents will be 900/ 900, that's a deal :) Good luck