It depends on what the div and the p are doing. If you're creating an extra one just to carry the class or id, you don't need it. If a div might contain more than one paragraph, then you've got two approaches:
<div id = "stuff" class = "otherstuff">
<p>blahblah</p>
<p>blahblah</p>
</div>
or
<div id = "stuff">
<p class = "otherstuff">
blahblah</p>
<p class = "otherstuff">
blahblah</p>
</div>
For the first version, the css would say
div#stuff {your styles here}
div.otherstuff {more styles here}
and optionally also div#stuff p {styles that should apply to any paragraph inside a div with this id}
div.otherstuff p {same}
For the second version, the css would say
div#stuff {your styles here}
p.otherstuff {more styles here}
and optionally also div#stuff p {as above}
In the last case, div#stuff p will override p.otherstuff if there's a conflict-- for example, if they each set a top margin. Don't mess about with !important declarations. Instead, say
p.otherstuff, div#stuff p.otherstuff {styles here}
so the CSS has no doubt what you mean.
