New To being landlord in owner occupied duplex

[Alex Alvarez]

Hello, I will be closing on a duplex soon that I will be occupying.One tenant will be moving out and the other tenants will be staying .I intend to sign new lease with them. They have been there since 2006 are on a month to month and receiving section 8 assistance. They are paying 800$  it’s about half of fair market rent...talking with an attorney and the (HA) housing authority I am able to raise the rents to fair market rent. I will be signing a 90 day lease and giving them a 90 day notice of rent increase at the same time . I will be increasing the rent to $1350. According to the HA that would have little or no difference to their responsibility for rent. I would appreciate any advise you can share. 

-Should I still do a background check? What I do know is, its an elderly lady with dementia  and a daughter that takes of her. the current land lord shared the last few of years and YTD payments from the tenants. (no late or missed payments)  

 -Do I simply go from getting keys, Changing the locks for both units and presenting a new lease to the tenants? when is the best time to present them with the new lease? 

- The home is out dated and when ever they vacate I will be renovating the unit. Do I require a new security deposit and first and last months rent? With the current times of the pandemic I really don’t want to add any financial hardships to anyone.(I do intend to increase the rent after the first year though) should I ask it a 1st and  last months and deposit? Can I even ask for those ? 

I appreciate any advise or past experiences you can share