You mainly said hard pen, not brush here.
Hard pen calligraphy paper is soft, slightly softer than A4 computer paper and slightly thinner than A4 computer paper. I forget the name of that kind of paper, well, it is the kind of paper used by primary school students. You can also go to the printing factory and ask them to cut it. That kind of paper is not expensive. 10 yuan is enough for you to write the first half of the year.
The two sides of this paper are different in texture, one is smooth and the other is rough. Use the rough side when writing.
Why do you want to write like this? Because the surface is too smooth, your pen is too slippery and the writing effect is not good. Slippery doesn't mean smooth. It is difficult to write fluently on a glossy surface, but it will be more slippery. I've tried this many times, so I don't recommend you to use A4 (double-sided glossy) paper.
On the rough side, no matter whether you write running script or regular script, because of the rough surface, your pen is not easy to slip on the paper, but it plays a role of "convergence", and the writing effect will be much more stable. Many strokes can be close to China's calligraphy.
As long as you understand it carefully, you will certainly understand what I said.
I have been engaged in calligraphy 15 years. I write in brush at home and hard at work, and I have used countless papers. This is my experience in using paper when writing hard words. But the method is different, and the landlord has to ponder it himself. I hope my reply is helpful to you.