Fusible interfacings will add firmness and strength to a fabric. It is easier and faster to work with fusibles than sew-in interfacings. However, certain fabrics, like velvet, do not fuse well. Sew-in interfacing can be removed and replaced making it a safer option when you are unsure about your interfacing choice.
The type of interfacing you choose will depend on what you want for the finished garment. Do you want a firm tailored look or something soft and drapable? Woven interfacing will add strength and stability. Knit interfacings are more flexible and have more drape. Non-wovens are the least likely to shrink.