I saw two interesting options today, both have exterior damage due to poor maintenance.Can someone recommend a contractor in the South Side of Chicago?

Just understand that as you go down in desirable area, you generally go up in rents but turn-over and risk of damage are greater.

What's the number one thing that causes damage to a house?

However, if the move-in deposit is only to be used to cover damage that happened while you were moving, you might have to pay out of pocket for the extra fine.The security deposit can only be used when you vacate to restore the property to pre-move-in condition or to cover any unpaid rent or fines incurred while living on the property. 

Also, several issues came up with insect damage and a sagging main beam and appliances that are end of life.  

Yes, this is a flat ground, no concrete left (sadly the demo guys damaged the slab and footings and removed them although engineer deemed they are sound for rebuilding).

While that might be useful if you want to evict the tenant, it could also result in damage to your property. 

I'm looking for some advice on where to go on this one without further damaging relationships, and not putting our family in a major financial hole. 

What damages do you believe you have incurred by the seller?

My initial thought is to charge a $35 service call plus repair costs IF the damage was a direct result from the tenant.