As a vacation rental, I helped them with furniture, installation, setup, staging and everything else to get the property ready for rental.

Arbitrage could still require significant capital to start off with for the furniture and charges associated with getting the unit (security deposit, first month's rent, etc.) plus reserves. 

Most young people make the mistake of getting in the "rat race early" after going to college, buying a brand new car, then trying to move into a fancy house, big fancy weddings, buying expensive furniture and financing everything under sun on credit then they work for someone or some company till their kids graduate college and never save a dime till the day they die.

Are purchases like furniture expensed or depreciated?

There are plenty of turnkey units that might just need some paint and a bit of new furniture. 

Can we write off the money we spent prepping the property (paint, new furniture, etc) this year on next years rental income?

I was contemplating leaving all the furniture and setting up a "room share" medium-term rental over a traditional lease agreement.

If you are not leaving the furniture, I would recommend long term rental. 

That's the purchase price of the foreclosure, plus the 4 appliances and furniture. 

We bought a ton of used great shape USA made furniture along with free stuff we found all over the internet.