Quick and dirty, add this to the index.html (Apache default site) in the root folder.
<script>
window.location.replace("http://myserver/mysite");
</script>
Then, when you are tinkering with mod_rewrite and mod_redirect, be sure to match the terminating $ (end of string) to avoid loops, like this mod_redirect only solution:
RedirectMatch 301 ^/$ http://myserver/mysite/
RedirectMatch 301 ^$ http://myserver/mysite/