I've printed my own fair share on Van Dyke prints.. I can tell you what worked for me.
I started with cyanotype, but honestly they aren't that similar. What worked for me with cyanotypes didn't work well for van dykes.

I use Crane's Kid Finish Ecru White stationary paper. $11 for a box. Once I tried this I stopped looking for any other paper.

I use a cheap 1" flat watercolor brush to apply the solution. $6 at an arts and crafts store, works perfectly fine.

I always add 1 drop of glycerin to the solution before coating the paper. It seems to make it easier to coat the paper. I also wet the brush with water first and lightly brush the paper to get it slightly damp.

If the paper is slightly damp, along with the glycerin.. it applies much more evenly and easily (at least for me).

I use cough syrup measuring cups, 5cc/10cc syringes with blunt tips, etc. to dispense the solution.
Sometimes I do two coats; I let the first coat dry halfway, while slightly damp I apply the next coat.
Often times I only need one coat.