At this stage of inking, I'm going through and doing all the characters. I find that you get into a kind of flow and don't want to stop and switch gears to do the backgrounds so I'll pile up a chunk of pages and when my hand gets tired I can take a break and do the bgs. Later, I'll do the bgs and props with a pen or brush pen (my subtle little trick to distinguish the characters from the bgs) so I can take them to a coffee shop or something and get out of the house. Doing bgs and objects is kind of boring to me so it helps to be doing something else at the same time. The characters are where the life and story is, which is another reason I like to do them separately and nicely with a brush and ink.
Below are my current inking tools. Windsor Newton India Ink($5) and a #2 Blick Scholastic Wonder White Round($1.50). Right now I'm inking up Chapter 6&7 with these and did the rest of the book with different brushes and ink - mostly what I could find at stores close to my place and what was the cheapest. I think the most I ever paid for a brush was $4 but can't really tell the difference. Once I bought cheap ink(Sumi Drawing Ink) and I could tell the difference, that stuff was watery and turned out kind of gray. I like the Windsor Newton and will likely stick with it, it does a nice black and goes on smooth. I'm looking forward to comparing pages and trying to see if a difference in materials made any difference in the art. Though, my hypothesis is: it's not the materials, but how tired or focused I was at the time!