Certain items just need more attention than others. What's worse is that they are usually found in every home. And so you would just have to deal with them properly as you prepare for the move. For instance, dishes and other breakable items are most often found in the kitchen. Because of this, you need to prepare a lot of bubble wrap, packing tapes, packing paper, peanuts and small or medium sized sturdy boxes. You cannot use large boxes as breakable items are generally heavy. You would want to avoid very heavy boxes so movers will have an easier time lifting them. This will minimize the chances of dropping the boxes and breaking your breakables. Make sure you securely seal the bottom of the box by taping it several times. Then line it with a layer of bubble wrap and even another layer of crumpled paper or peanuts. Wrap each dish with bubble wrap before you put them in. Make sure there is a bubble wrap or at least packing paper in between each piece and don't forget to seal the box well too.
 
Plants and pets need special care and attention too. Many removals company would not transport them for you though. And among those that accept plants and pets, many would not cover them too. Flight regulations and city or state laws could also prohibit you to bring them. You would have to ensure they are allowed before you pack and prepare them. Because of this it is essential that you make reservations for the trip in advance. You should also ask your apartment manager about their regulations.