The traditional method of coating albumen paper is to float it in a tray. The emulsion has to be applied to the paper in one smooth motion or you will get wicking effects. My impression from those who have tried it is that it is just not possible with a brush--you'll always get brush marks. Some have had success with a coating rod.
I float, and it works for the most part. What I do is steam the albuminized paper over a kettle until it is supple and then roll it albumen side out and let it sit that way for a few minutes in the core of a paper towel roll. Wearing nitrile gloves, eye protection, and an apron, I check the tray for bubbles and push any to the side with a strip of scrap paper, then I hold the far edge of the paper between my thumb and index finger close to the nitrate solution with my other fingers resting on the far edge of the tray, then release the paper and float it on the solution in one motion, making sure the edges are in contact with the solution and that the solution doesn't get on the back of the paper. After three minutes, I pull it out smoothly, drain the excess over the tray, and hang it on the line to dry with two clothespins.
One-ply paper is much easier to work with than heavier paper. I use Strathmore 500 1-ply. I've experimented with two-ply and gotten some good ones, but the rejection rate seems higher. Maybe with practice one could get the hang of it, but almost all traditional albumen prints are on thin paper. Here's a 4x5" on 2-ply--
To make the silver solution go a long way, get some kaolin to clear the used solution, decant, and reuse it. The process is described in Reilly's book.