Trying keeping existing tenants or starting from the beginning

[Eugen Burianov]

I am buying a duplex that has tenants which I didn't pick and didn't do the due diligence on them (security deposit, background checks, etc) to minimize the risk. The handyman mentioned they seem to pay rent regularly.  The house needs quite a lot of repairs. My dilemma is to either:  

 - continue with current tenants, try to accommodate the repairs with them but risk from not having done enough check on the quality of tenants. Will it be harder to terminate their rental later in case it doesn't work out?

OR

- terminate their rental after I close on the deal, do the repairs and look for tenants all over again.

I am worried that it might be harder to terminate the rental with them later, I kind of have an excuse now that I am buying the house and want to make repairs. Does this timing really matter though, is it likely that it will be harder to let them go later if they turn to be problematic tenants? Or it makes sense to give them a chance to prove themselves as great tenants?