A lot of templates are used to output a single Views display. It depends on your particular case which level you want to override. These templates are probably the best way to control the output of the views where ever you want to print them.
One template outputs the outer views divs, another is for particular format options, others are for controlling rows output. So you have to investigate and override the templates where you want to change the HTML for that particular view.
You can strip each individual Field of its wrapper and even field HTML in its
Style settings directly in Views.
You can see the template suggestions under
Theme: information in D7 Views, and in D8 you have to turn on the debugging mode to see the suggestions in page output.