The live plants are always going to look better than plastic, as you are seeing in your tank. The plastic mesh pots with stuff around the roots are just to allow the grower to grow plants partially emersed and easily lift them from the water to ship out. The usual practice is to remove the plastic mesh pot by cutting it off, then remove as much as you can of the material that is packed around the roots. Be careful with the anubias, they do not take well to having their rhizomes buried in the substrate, it kills the plant. Plants that have been growing emersed will become softer as they adapt to being fully submerged. In the case of Crypts, they often will lose all of their leaves in the process, then grow new ones that are better adapted to underwater growth.