What is a good brush or comb for my house-kept hound? Should she be brushed/combed in both directions, or just with her coat?
The type of dog and coat depends on the type of brush that you should use. This dog grooming site has good information on the types of brushes to use for the type of dogs. From my own experience, when my lab was between the ages of 2 months to 18 months, I was told by his vet to use a rubber brush or a soft brush, like so:
Now, when he is older than 18 months I have been using a brush similar to an undercoat shedding rake. Honestly, the type of dog and type of fur dictates what type of brush you use.
I have bedlington terriers which have curly non shedding coats. I use a slicker brush in both directions and I have a stainless steel comb to check through the coat. Even brushing well can leave mats and running a comb through against the hair growth is a good double check that you have got out all of the tangles. Important for any long haired or curly dogs. Mats probably won't be an issue with a short haired dog but I would still use a slicker brush.
Brush with the coat, brushing against it can be uncomfortable for the dog. Find a good brush. Something like this https://www.rayallen.com/evolution-self-cleaning-slicker-brush/