Fountain pen ink is more watery than the ink used in many other types of pens, and fountain pens put a lot of it on the paper. The combination creates a challenge for the paper that makes it difficult to have the "perfect" paper in every respect. You typically need to choose what you want to optimize, and use a paper that optimizes that.
The challenges created by fountain pens and their ink
There is a lot of very liquid ink applied to the paper. The liquid dries through absorption and evaporation. If it is heavily absorbed by the paper, it spreads sideways (the lines get wider), and it "feathers" (feathery bleeding so the line edges aren't sharp). It also soaks into the paper, which can cause it to bleed through to the back (you see some of the ink on the back surface, even the front surface of the next sheet).
If the ink is kept controlled on the surface of the paper, a lot of it requires evaporation to dry, which is a much slower process. As long as it's wet, it can smear and get picked up by your hand (and transferred to other surfaces). But once it dries, you get the crispest lines. In some cases, this can allow you to see a sheen, which some people find desirable. Even though the ink stays mostly on the surface, there is a lot of it, with a lot of contrast. If the paper is not fully opaque, you can see "ghosting" of the writing through the paper on the other side.
There are characteristics that make paper more fountain-pen-friendly. Heavier-weight paper helps with bleed-through and ghosting. Smoother paper reduces its absorbency (the fibers are more compressed). Sizing (chemical treatment, not the paper dimensions), and coatings reduce its absorbency so the ink doesn't soak into the paper as much.
However, while super-smooth paper produces crisp lines, it also eliminates most of the friction of the pen nib on the paper, so you lose that feedback -- the feel of the pen moving on the paper.
So there are trade-offs in fountain-pen-friendly paper. Some people want the best possible lines. Others want more of the feel of the writing experience as long as they get good-enough lines. The crispest lines also tend to be more slow-drying. The best-optimized papers are somewhat niche products; they can be expensive.
You can expand the range of papers that will work well by using fast-drying ink and/or a finer nib.
If you use ink with a very rich color, you might also want to use paper that is extremely white.
If you're starting from scratch and want to try some random papers that you have ready access to, the best results will generally be with very smooth, heavier-weight paper, so start with those. But not all of them will be good, and there are lots of exceptions. Much depends on how the paper was made. It doesn't hurt to try almost any paper you can get your hands on just to see the results.
Fortunately, fountain pens have a dedicated following. There are lots of web sites devoted to using them. Among aficionados who have explored the available papers, a relatively small number of papers have risen to the top. I'll include links to a number of sites and paper evaluations and preferences (some have more detailed descriptions of the papers and the specific version recommended; some cover different "formats", like notepads, stationery, journals, etc.).
A large number of lists have these papers at or near the top (in varying orders): Tomoe River, Rhodia, Clairefontaine (made by the same company as Rhodia), and Midori, Also near the top of many lists was Oxford Optik. One that made a number of "favorite" lists because it generally works pretty well and is inexpensive was HP Premium Laserjet Paper (especially 32 lb).
Many stationery stores will provide, on request, a sample pack of a mix of different papers of interest (a few sheets of each one, typically either free or for the cost of postage). It's a good way to compare high-end papers without spending a lot of money on full packages.