You have to be careful about putting somebody's stuff into storage - it's you who will have a contract with the storage facility, so it's you they'll come after for unpaid storage fees.

Take pictures of everything. I recently helped a landlord who was accused by a tenant of destroying lots of valuable property. The landlord's photographs established that the only things discarded were garbage. The landlord had its own storage shed and put anything that wasn't garbage into storage pending the outcome of the court case; most individuals don't have that latitude.

With the eviction order, the tenant's belongings can be put out of the house (often curbside) for the tenant to collect. Often from that point they are looted by people who think they're abandoned (or just don't care whose they are), but that's no longer the landlord's problem. It can be costly to use a court officer for this process - but you're supposed to have a court officer present, so look into the comparative cost of providing your own laborers and having the court officer serve as a witness to the eviction.

If the tenant wants his belongings at a particular place, he can collect them and move them where he wants beforehand, or pick them up when they're curbside. Other than as necessary to evict him, you don't have to move them for him.