I am curious as to what dynamic range can be achieved with, let's say, glossy vs. matte paper or other media such as metal or acrylic prints.
It is really complicated because you need to compare brands and systems with the same reference image.
This will be an answer just based on my little experience.
In general terms the paper must be coated. The quality of the coating has an effect too.
From less vivid to more vivid:
Newspaper. (Matte, not white)
Bond paper (normal office paper). (Matte, different levels of brightness)
Special "Inkjet" (for presentations and reports) (Matte)
Photographic paper. (glossy, satin). (In large formats vinyl based should be arround here)
Synthetic based photographic paper. (glossy, satin)
Rotary offset (this can use the same inks as sheeted offset, but normally the paper has less quality)
I am not sure where true photographic prints are related to the inkjet based ones. Probably here.
Inkjet based systems have in general terms more color range than offset and laser.
On large format latex based plotters are better, and smoother than other systems.
Number of inks
On an offset sheeted commercial print there was a hexacolor system which is no longer supported.
On a 6 ink inkjet system there is not much difference, because the additional inks are light cyan and light magenta, not orange and green.
Pantone or spot inks can be out of the cmyk range.
UV bright one make the colors more vivid than matte one. The same is true for plasticized.
Normally these have less vivid colors, because a good part of the light is reflected by the metallic surface, and the inks are more transparent, so you can see the metallic part.
Like Rafael has written, it's not so simple answer. But if you need to choose between glossy vs. matte paper, glossy is the winner in 85%.
Which print medium has the highest dynamic range, well the answers is the medium with the most neutral white colour - meaning actual white without any colour cast, any discolouring will reduces the actually dynamic range of the medium. However, the printers resolution, number of colours and colour pattern is the most important aspect of dynamic range on print.
Coatings have little to no effect on dynamic range, however colour reproduction looks more vibrant on glossed paper.