Plugin frontend page design irrespective of the theme used

I don’t know which CSS styles/classes can be used.

You can’t know this, not without knowing which plugins and themes there are installed. Prefix your classes so they’re unique and it becomes a non-issue.

And if I use my custom CSS styles that may look awkward with the current theme.

Someone somewhere can write a theme that will look awkward. This isn’t a WordPress problem but one of CSS specificity.