Did you install it into a subdirectory under public_html/, such as public_html/eStore/? If so, good -- leave it there. If you want a visitor to see your own Home Page first, just put a link into public_html/index.html (your Home Page) to go to /eStore/index.php. If you want your visitors to go directly into your store, either do a redirection in cPanel/.htaccess to go to /eStore/index.php, or use the following public_html/index.html:

Yes, I strongly believe that every major subsystem on your site (store, blog, forum, gallery, other pages) should be installed into its own directory under the site root. I leave the site root empty except for an index file and site support files such as error pages, robots.txt, favicon.ico, etc. This gives you flexibility... even if you currently plan only to have a store, what if in the future you want to add a blog or forum so customers can rave about how good your products are? The only downside is that while you have only one subsystem on your site (say, a store), it's an extra step (through redirection, a dummy index.html with a meta tag, or a splash page with a link) to get to your store. I think that's a small price to pay for having everything cleanly separated, rather than all mixed up together (if that's even possible) or cluttering up the root. Fantastico tries to prevent you from installing everything into the same directory (e.g., site root), but a manual installation could result in your wiping out files belonging to another subsystem. Keeping them separated makes it easy to upgrade or delete a subsystem, or replace it with another implementation. That's my two cents on the subject.