He also wants to sue for damages of mattresses thrown out, furniture, etc.  

This is not only because pets sometimes will damage the furniture.

The agent we like seems to think that houses sell better with furniture in there, as long as the person is neat, doesn't have ridiculous style, and is willing to allow the agent to show it to buyers.One of the other agents suggested we try to sign the tenant to a 6-month lease and sell it in late Spring/Early Summer.Thoughts? 

-Unless you want kiddos breaking your beds during every turn over, don't go cheap with the bed furniture for kids if you plan on having twin beds, etc.

Keep in mind that most buyers cannot envision how rooms are supposed to be used, so you need to tell them through staging, if you are using furniture, or through obvious cues (i.e. flat screen TV) in lieu of furnishings. 

What about if there is old furniture inside?  

The all-in costs including material, labor, permits, foundations, etc excluding your furnitures is around $120 - 150k.

It won't hurt to offer "partially furnished" units (fridge, microwave, stove and maybe a bed - there are a ton of places to find fairly nice furniture without breaking the bank).

They can also provide coatings to reduce the amount of UV which enters (protecting your floors and furniture). 

Used a furniture leasing company (Aaron's) that was $220 a month.