Regarding paper for alt process printing, it is my belief that more beginners are turned off from alt process printing by using cheap paper. Sure there are some cheap, chain art store papers that work but there are many more that have issues with various processes.
Furthermore, these no name or store brand papers change properties (sometimes with a change in packaging, sometimes not) without warning and more often than you might think. These store are looking for the best price not for consistency when they go to purchase a lot of paper.
When I teach workshops, I recommend that folks stick to paper from the big mills to avoid, well minimize, paper problems when starting down the alt process path.
Thus, I am a bit surprised to hear the comments about papers from Magnani. They are a smaller, but well known mill. But I don't have any experience with any of there papers., so I can't be of specific help.
I also tell folks that if you try a paper and it does not work well for a process don't spend too much time trying to get it to work. Rather, just move on as there are many other choices out there.
That said, for cyanotype my go to paper is Fabriano Unica White (it comes on other shades), a decently heavy (250 gsm) 50% cotton printmaking paper. Another inexpensive paper that works well with cyanotype is Fabriano Studio watercolor paper (300 gsm, 25% cotton; I think that there is a lighter version available as well).
More recently, I have also been using Hahnemühle Bamboo Mixed Media (265 gsm) for cyanotype. This paper is not as smooth as the other two and is a bit warmer white, but the texture is subtle.
All are available in pads/blocks as well as large sheets. (However, I've yet to find a source for sheets of the Bamboo Mixed Media paper in the US.)
I do not pre-treat these papers to remove the carbonate buffer when using them for cyanotype. Rather, I 'develop' my cyanotype using 10-15% (v/v) vinegar in the first tray before extensively washing the prints. This gets rid of the carbonate quickly enough that the Prussian Blue is not significantly hydrolyzed and it helps with the contrast in the mid-tones.