I've worked with Joomla and have noticed that the major concerns when changing templates isn't the class names, ids, etc but more the architecture of the code. As an example if you are changing from a template that has the majority of the page's content "above the fold" to one that does not, I would expect to lose a notch or two in search results. Another thing you may want to consider is what kind of navigation structure you choose to use. content's still king, but if search engines have trouble crawling (or can't crawl some pages) even though they are currently ranking well you may lose some rank.
Not trying to scare you sir, just pointing out the "red flags" that usually come up.
Hope it helps!
if you're using a menu like this, make sure you leave another way for the search engine crawler to get to the parent item on your pages.
<a href="#">Parent Item</a>
<a href="page1.html">child item</a>
<a href="page2.html">child item</a>