To Keep an inherited tenant or ask seller to remove?

[Alicia Gates]

We're looking at purchasing a SFH in our area, and it currently rents for $650, but market rents are $850-900 in the area. The house looks to be in decent shape, but there does seem to be some cosmetic items to be fixed.

The sellers want to close quickly and want to know if we plan to keep the tenant or ask the seller to give them notice to leave.  I don't have any information on the tenant other than they "might" pay more in rent.  The sellers want us to have a meeting with the tenant to see if we would keep them. 

What questions should I ask or things should I consider if I think about keeping the tenant?  Some things I'm thinking: 

• How long have they been a tenant? 
• What was the screening process?  Is there a background check?
• Do they pay timely - every month? 
• Who pays utilities? 
• Who does yard maintenance? 
• Do they have pets ?
• Do they smoke? 
• What are the lease terms?  (I've read elsewhere that month-to-month is what I would wish for, so I could remove them myself if need be.)
• Last, since it's fall, is it better to keep a decent tenant at well below market through the winter and then remove next year during a more favorable leasing season (assuming lease terms allow for this)?

I'm leaning towards telling the seller to ask the tenant to leave so we have a clean slate, but I don't want to shoot myself in the foot either.  This will be my first rental.  Thanks!