Usually movers assist you in packing if you demand for. Many moving companies in Houston provide this service to their customers. Besides moving these moving companies locate Houston apartments according to your requirements.
As suggested;

Packing must start with one room at a time – by labeling every box with brief explanation of its contents and the destination.

Don't dump many things in a single box. Heavy items are suggested be put up in the small boxes so as to keep away from various hassles of carrying.

Applying tape directly to the wood or any painted surfaces is not recommended- As it might damage the surface or paint.

Cushioning is another major area of concern while packing the fragile belongings and especially when planning to move from Houston apartment.