Coarse individual hairs? I have that - average number of hairs, probably, but thick because each hair is thick. I use now Innersense Hydrating Cream Conditioner. Have never had anything work this well before, it's like it was made for my hair. Super concentrated, very expensive but I buy the liter bottle and it lasts half a year.

Shampoo, I don't think it matters as much, doing it less often matters more. Anything reasonably gentle, low or no sulfate (look for other surfactants higher on the ingredient list) If your hair is naturally dry, not damaged (coarse hair often is) then getting a good conditioner and leaving some in will make the most difference. If it's dry from damage then a protein treatment might work better.