Pull from Database directly/formatting issues

I have created some very simple PHP-based pages that pull information directly from the word press database. I know I could hack around with the regular WP pages to get what I want, but what I need is so simple I’d rather create it from scratch.

And I have my page working fine EXCEPT I can’t figure out how to correct the display problems with quotes, apostrophe’s and other symbols with text copied from Word. I’m using Markdown, so I get the paragraph breaks OK, but that doesn’t fix the problem with symbols. When I look at the posts through WP they come out fine, so I know there is something else I’m missing.

Can someone point me in the right direction or provide some helpful pointers? Even just having the example of which code in WP handles this would help me figure this out.

Thanks