whenever I hyperlink an image, a purple or blue border surrounds it, showing that it's linked to another page. How do I get rid of that border?

Try this:

<a href="link" border="0"><IMG SRC="Image"></a>

the border="0" worked in the image tag, not the link tag.

To have no lines under the links....

see:
http://www.lissaexplains.com/css.shtml

or this generator:
http://www.ahfb2000.com/cssgenerator.php

(If you don't like that generator, just do a for CSS+Generators on www.google.com to find them.)