When choosing a paper there is no real right and wrong with surface types, as almost all can produce excellent results. It really comes down to the image you have chosen and the look you want to achieve or final mounting method.
Gloss and Metallic Gloss Papers
Gloss papers have very smooth, highly reflective surfaces. Inherently, they offer the punchiest images due to their extremely strong blacks. The glossy surface can however be prone to scratching so these papers are not ideal for handling.
Resin coated papers have a layer of smooth plastic in them so tend to be the smoothest and thus most glossy.
Fibre based papers always have some structure to them so they never quite achieve the same level of smoothness. However they tend to offer greater archival properties.
Very glossy papers can be difficult to frame due to the increased tendency for reflection issues when behind glass.
Ideal for coloured high detail images.
Semi-Gloss - Pearl and Lustre Papers
Semi gloss papers have a slight reflective texture but are very robust and stand up well to handling. The surface tend to hide minor imperfections like finger prints and slight scratches.
They offer very deep blacks and have moderate reflection issues when mounted behind glass.
Again, they come in both resin coated and fibre based form. In this category, resin coated has no real advantage - they are just cheaper because they are made using plastic rather than fibre such as cotton.
The perfect all-rounder and go to paper when in doubt. Ideal for coloured images.
Matte Papers are truly matte, sometimes called ultra-matte or water coloured papers, and have no reflectivity issues at all. They do however have somewhat weaker blacks.
To combat this, the use of papers like the excellent Hahnemuehle Photo Rag offer very good blacks that stand up well to normal diffuse lighting conditions.
Smooth matte papers are the very best papers at letting the image speak because there is no surface texture or reflection to interfere with the image.
Textured matte papers can be quite beautiful and particularly with simpler images the paper texture can really add to the substance of the image presentation.
Typically used for black and white fine art images, however also suitable for coloured images. Perfect for the purist with an art paper / card like feel as opposed to the plastic photographic paper options.
The perfect choice for black and white images.