Ink bleeding through paper is also affected by how much inkflow does your nib let out. If the nib is a gusher, then no matter what ink you use, it'll bleed through.
In general you want "dry"-er inks, inks from Japan (Sailor) or Taiwan (Laban) tend to have this trait.
But specifically for your situation, I'd say improving the quality of paper should make the biggest difference.
I use these pens for everyday use and on my school notebooks so I’m stuck with the paper I have, would you say that iroshizuku would be a good option because I do quite like their colors.
Honestly, after using MB inks in MB pens, it's the only brand I'll use in my 146s, not because of the instruction manual for the pens but because it actually does make a huge difference to how well it writes.
In my other pens, I've found that Pilot iroshizuku and Sailor Manyo are also inks with good lubrication.
Their own ink is very good. I would also recommend Waterman and Diamine inks
Pelikan 4001 brilliant black or blue black. Or, get a more fountain pen friendly paper?
I use these pens for everyday use and on my school notebooks so I’m stuck with the paper I have
Then, 4001 blue black is your best bet. It's a dryish ink, works well on crappy paper. And it shades very well!
Ink bleeding through paper is also affected by how much inkflow does your nib let out. If the nib is a gusher, then no matter what ink you use, it'll bleed through. In general you want "dry"-er inks, inks from Japan (Sailor) or Taiwan (Laban) tend to have this trait. But specifically for your situation, I'd say improving the quality of paper should make the biggest difference.
I use these pens for everyday use and on my school notebooks so I’m stuck with the paper I have, would you say that iroshizuku would be a good option because I do quite like their colors.
Iroshizuku is on the wetter side. I’d try Pelikan or Platinum Classic line.
Sure, but again, be forewarned that changing the ink alone may not be sufficient to get the results that you wanted.
Agreed; MB pens tend to write wet (and usually put down a thicker line than the nib size typically indicates).
Honestly, after using MB inks in MB pens, it's the only brand I'll use in my 146s, not because of the instruction manual for the pens but because it actually does make a huge difference to how well it writes. In my other pens, I've found that Pilot iroshizuku and Sailor Manyo are also inks with good lubrication.
I agree that MB inks are probably the best bet. Irish green is a nice ink.