If you are renting now and moving to a new address, your main concern really is to move and still be able to claim your security deposit from the landlord. To be able to do this you must restore and leave the apartment or the house the way it was when you first arrived there. That is why you must make simple repairs on the new place. For instance, you have to fill holes you have punched for nails. If wall paints have faded or become uneven, you may also have to repaint the walls.
After doing the repairs, you also have to make sure that the whole place is clean. Otherwise, the landlord would have a reason to make you pay for the cleaning services. This would again prevent you from getting your security deposit in full.
Even if you own the current place, you would have a reason to clean and repair as well. These are necessary to attract potential buyers. It could even raise the price of your home. 
Make sure that your things are insured for the move as well. Always clarify what type of coverage is offered by the removals company. If you have big, expensive and delicate items, you would have more peace of mind if you invest on more coverage.