How well a fountain pen writes on cheap paper depends very much on the ink. Several years ago, when I first became interested in fountain pens, I exchanged ink samples with other enthusiasts, and tried many different inks. I had the best results with Noodler's Black, which avoided feathering or bleed-through even on cheap paper. I got through a 3oz jar of it, and I'm currently using a 3oz jar of Noodler's Bad Black Moccasin, which I don't like as much. Next jar will be the normal Noodler's Black again.
Nib size also makes a difference; this was with an extra fine nib on a Lamy Safari.
I'm currently working my way through a bottle of Noodler's Dark Matter. Really well behaved ink, though I'll likely trade-up to Noodler's X-Feather (anti-feather black) or plain black.
I have samples of Noodler's 54th Massachusetts and Lexington Gray that I'm looking forward to trying.
Nib size also makes a difference; this was with an extra fine nib on a Lamy Safari.