You can somewhat narrow down the choice of papers to try by reading others' impressions as well as the manufacturers' descriptions. Specs like paper base, weight, and thickness can greatly affect the impression a print makes when handled. The presence or absence of OBA's are also worth considering if you're selling prints and have to worry about permanence. But in the end you really just have to try some different papers to find the one that best meets your needs. Fortunately sample packs are available for many papers to make the process a little less painful.
On the matte versus semi-gloss issue. For me I really like matte papers when texture is important to the image, or when the more painting-like effect of the matte surface complements the image. For some images, the matte paper really enhances the apparent depth of the image, due to the lack of any surface reflections. Of course, once framed behind glass, much of the benefits of matte paper can be lost unless you're very careful with the lighting or use a high-end glass with anti-reflective coatings.
I tend to prefer semi-gloss papers for high-contrast images or images where deep and/or strongly saturated colors are important. The gamut in dark colors is much better on these papers. I prefer semi-gloss for images with reflections, because I think a matte surface can take something away from them. I've also found the semi-gloss papers a little easier to handle (though from what I've heard some of the higher-gloss papers with extremely smooth surfaces have their own problems with denting).
I've made the semi-gloss paper my default just because it simplifies things somewhat. For people who aren't familiar with matte inkjet prints, the semi-gloss print is probably going to be more along the lines what they're expecting from a photographic print. But I do offer matte prints for those who want them, and may even occasionally recommend it for specific images where I feel strongly it's the better choice.