For a plain two bedroom aimed at a traveling healthcare worker, most operators land somewhere between $8,000 and $15,000 all in, and the spread inside that range is mostly about how much you buy new. Beds are where people spend real money and should, because a bad mattress is the single most common complaint in a 90 day stay. Everything else can be secondhand without anyone caring.
The $5,000 figures usually come from someone who already owned half of it or who had a lot of time to hunt. The $25,000 figures usually involve a designer and a market where the tenant is a relocating executive rather than a nurse. Your tenant on a 13 week contract wants a good bed, working wifi, a real desk, and a kitchen with actual pots. They are not evaluating your throw pillows.
Budget separately for the stuff that isn't furniture. Linens in duplicate so a turnover doesn't wait on laundry, basic dishes and cookware, a decent lamp in every room because contract workers are often awake at odd hours. Quill is right that this pile adds up faster than the furniture does.
On the tax question, furniture is generally treated as personal property with its own recovery period rather than being lumped into the building, and some items may be expensable in the year of purchase depending on current rules and your situation. That's a question for your CPA, and worth asking before you buy rather than after.
One thing to plan for now: where does the furniture live if you decide to switch that unit to a long term lease? Storage costs real money, and selling used furniture recovers very little.