I've printed on a number of papers for shows (a mix of photographic process paper and inkjet). Cotton rag can impart a soft, water-color texture to an image but cover glass will greatly diminish the effect unless one is up very close. It works with certain images, usually pastels with large blocks of solid or semisolid color.
Fuji Pearl can work well on images containing substantial blue water (the blue appears to "float" a bit above the surface). Canvas prints work best for me to create an oil-painting effect. Most prints work well on standard Fuji photo gloss paper on a Chromira or LightJet type printer. I'm not as fond of metal prints as most people are, and I personally don't like unframed pieces except canvas wraps.
The problem with buying/storing specialty papers is whether you'll have enough images to justify keeping the stuff around the office/home.
I use printing services to do prints and recommend the same to folks who want something better than a 13" x 19" cheapo print as printing with great quality is a separate craft from photography. If you like having two hobbies/jobs, and don't mind wasting a lot of time and paper and ink to become a master printer, go for it. But many great US printers will do a cost efficient, superior job on 16" x 24" or 24" x 30" prints you'll frame and treasure for years. For many artists and hobbyists it doesn't make financial sense to spend oodles of time and money getting good at printing unless they love to do it. Before folks head down that road, I recommend they consider carefully how many actual prints they will produce, what they will do with them, and translate any labor hours and estimate printing practice costs in $ so they can compare apples to apples (you might consider the space consumption as well). There are too many people who bought into expensive 24" or 44" printers and framing equipment and regretted it as it dragged them away from what they loved to do and was more expensive than even the best professional service for the number and kind of prints they wanted.