if(strstr($HTTP_USER_AGENT, "Mozilla")){$user_agent = "Mozilla";}
if(strstr($HTTP_USER_AGENT, "Konqueror")){$user_agent = "Konqueror";}
if(strstr($HTTP_USER_AGENT, "IE")){$user_agent = "IE";}
and
echo("<link rel='stylesheet' type='text/css' href='stylesheets/stylesheet_".$user_agent.".css' />\n");
into the .php file. This way of course doesn't work if the user chooses to mask his/her browser as anotherone but that is more or less out of ones control. This also means that the CSS files have to be named like for instance "stylesheet_Mozilla".
Oh, and thanks sunsnapper for the tip about sizes. I was looking for that somewhere.