Redirect root to subdirectory w/o subdir name in link??

I am a newbie and have WP 2.8.4 installed on https://www.mysite.com/wp
I wrote a meta redirect index.html page to direct mysite.com to mysite/wp . My current links shows as
for category : mysite.com/wp/category/cat-name
for post : mysite.com/wp/year/month/post-name
for page : mysite.com/wp/page-name

I could live with this but I want to find the absolute proper way to configure my site so it will not show “wp” . I have searched and there were so many option listed which confused me. I just want to know what is the WP recommended approach to do it right .

One other question – do you redirect subdirectory to root or do you redirect root to subdirectory and do some WP config ?

btw, I have tried to use my cpanel redirect and that gave me nightmare. This redirect was working fine up till my permalink setting. I believed there are some conflict of sort between cpanel hta and wp hta , I do not understand as why as both reside in different location .

Greatly appreciate any suggestion. Thanks!