Get the easy stuff first - rent roll and lease end dates, any bills the landlord pays - common area maintenance, maybe water, sewer, taxes, and insurance.

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Purchase price: $242,500 Cash invested: $49,000 This is an older house, built well on concrete block, that is next door to multi-million dollar houses on the water.

Water heater 12 years to replacement (may need some service before replacement).Recognize many cap ex items are years away.  

I'm just curious should I furnish the place or just keep it empty and people can move their own stuff in and just drop the minimum lease duration to 3 months?   

There is always a chance that rates will drop, but I would imagine $25K would buy down the annual rate so significantly that you would never see a lower rate offered by a bank so you wouldn't even think about refinancing.

The main issue with rental basement is water if it has water issue usually it is a simple fix .Clean gutters ,discharge gutter  water away 10" away from foundation, make sure you foundation soil is slopped away from it .If you need to buy soil get a clay mix .Cut back any tree too close to the foundation look at the drip line that's how far the limbs are out from the tree .If all that is done still has water buy a sump pump  carry the water to day light away from foundation 10" to 15" .

The more you drop the price, the bigger the issue with guests will be.

i buy flooring at a discount and drop it off at the property. 

Water services.