There is no harm in a plain CSS file, and applying classes at the element level in the HTML.
If you put in-line CSS in the HTML is not only leads to severe duplication, but is also a maintenance nightmare if you want to change anything. It works fine if all you are changing is a colour or whatever, but often there are margins, paddings, letter spacings, font sizes etc etc which lead to quite a lot of extra crap in each element on your page. Repeating those all over each if your HTML files is a real burden. Just use a single CSS file with sensibly named classes - it doesn't need to be sass or anything, just plain CSS is fine.