If you are not sure, keep it with a single, basic paper until you know. It would be like making the photo without deciding your subject and what you wanted to say. There are hundreds of options for papers - each of which can suggest different post processing. Pick one or two papers and just use them until you have a clear need for something different.
The first decision is usually the finish - gloss, luster, or matte.
Gloss emphasizes sharpness, sharp detail, and high resolution. The downside is reflections, fingerprints, and in some cases a common "drugstore print" feel. This paper is not commonly used by professionals these days but has in the past.
Luster eliminates or reduces some of the negatives of gloss paper. The finish is a little softer and less reflective, but it shows the image nicely. I'd put in this category very fine textured papers such as velvet finishes as an upgrade. You could put Baryta papers in this category. Both velvet and baryta papers are very smooth but don't have the glare of gloss. Sharpness is still seen in your image, but does not dominate. Metallic papers fall into this category.
Matte papers, fiber, and canvas all are textured papers. The paper becomes part of the image. Hot press fiber tends to be smoother than cold press. These are art papers that are often sheets only rather than rolls. The papers have a heavier feel to the touch. You can use these papers to convey the feel of a watercolor, an oil painting, or to minimize reflection.
Another aspect to this is the degree of whiteness in the paper. Papers have measurements of the reflective properties or the brightness of the paper itself. The catch is the whiteness is achieved with optical brighteners, and these brighteners fade in time with exposure to UV light. When the brighteners fade, the image can become dingy and lack contrast. So print life becomes a factor - especially dependent on where the photo is displayed. You may still want bright paper with optical brighteners - just avoid display in a bright area or with harsh lighting.
Paper weight is another factor. You have both paper thickness and the weight of the paper. Some papers are thick and need to be manually fed through a printer. Others are heavy or light weight. I try to stick with papers that are 260 grams or heavier, but at 320+ grams they normally require sheets to be fed manually. There are papers that are just 190-210 grams - but they are very light weight to the touch and I avoid them for photos.
As you can see, there are lots of options. Each manufacturer has variations on these parameters with small differences.
My suggestion is to start with something generic and relatively inexpensive but not cheap - Epson Premium Luster is my starting point since it matches my printer well and that eliminates some variables. I also use Canson Baryta and a handful of other papers, but added those slowly over time. At this point, you probably don't know enough to buy more than one or two papers.
