You can't see the Materia until you turn the Equipment into Materia, as the process is random (as in the Grade and the type of Materia you can get), but it's not totally random. Higher level produce higher grade, and a type of equipment can produce somewhere from 1-3 types of Materia for example, not all of them.
Only New Item, Unique Vintage and Dodore/Buffalo/Goblin/Uraeus/Mosshorn drop can be melded for Materia. Low tier NM, Grand Company, Toto-Rak and Darkhold drop can not make Materia or melded with Materia. Dated gear can make Materia but can not meld with Materia.