Inherited tenants...first time landlords

[Madeleine Austin]

Hello! My husband and I just closed on our first rental property. We are inheriting tenants whose lease is up at the end of the month. We were under the initial impression that their intent was to move out. Now we have heard they are looking to stay. We have not called to introduce ourselves quite yet.

They have a good reputation in terms of paying on time. However, the house needs significant work and for safety reasons, it is likely it will have to be vacant for 1-2 months as that happens. Additionally (I need to follow up on this), there are more people than I think are safe living on the property and they own multiple dogs...both conditions we were going to deal with when we create the new lease (still deciding the direction we are heading in). The previous buyers, in my opinion, were poor landlords. They clearly did not care for the safety of their tenants and made cheap temporary repairs. 

My husband and I still have to discuss (he returns home Saturday and is not reachable until then), but what are some things we should consider? Any advice? I know I lean in the direction of starting fresh and vetting our own tenants. I know my husband will be more concerned with the bottom line and the figures. He is more "a bird in the hand" but I am more cautious (sometimes too far). Any advice from seasoned property owners?