I've recently been converted to bullet journalling and, a few months in, I think I have formed my perfect kit for using in my Leuchtturm1917. Here are the best tools (writing-utensil-wise) for bujo-ing.
1 - Faber Castell Pitt Artist Pens
These are a firm favourite in the bullet journalling community. I bought this little set from amazon with a very teeny one (S) which is perfect for writing along with the 'F' pen, the 'M' is great for drawing in lines and the 'B' is useful for titles. They don't bleed and dry really quickly. They are slightly visible through the pages in the Leuchtturm, though not noticeably.
2 - Muji Gel Pens
These are far more easily accessible if you're London-based like I am. I LOVE the 0.38mm for writing notes, as it's super skinny and neat, and the 0.5mm for bolder statements, however these do take a tad longer to dry so can smudge a little if you're not careful.
3 - OhhDeer Biro
I use this to just write in any notes and plan ahead (not for main spreads etc) as it's really easy to write notes quickly, however these Ohh Deer pens are super black (unlike grey-tinged Bics).
I also use the ever-so-handy Uniball Signo Pen in White to cover up any mistakes - it's like super precise Tipp-Ex. To add colour, I use these super cheap pencils from my local pound shop and Staedtler Colouring Pens to add bolder details, although I'm considering investing in some of the infamous Tombow Brush Markers - any comments?