You might want to consider storing the user's selection in a cookie. This is easy using JavaScript. You can simply read from and write to document.cookie to do so. Also see this answer concerning reading a cookie.
Something along the lines of
function storeStyle(style) {
    var cookieSubStrings = [], cookies = readCookies();
    cookies.style = style;
    if (!("expires" in cookies))
        cookies.expires = (new Date().getTime() + 30*24*60*60*1000).toGMTString();
    for (e in cookies)
        if (cookies.hasOwnProperty(e))
            cookieSubStrings.push(e + "=" + cookies[e]);
    document.cookie = cookieSubStrings.join("; ")
}
var style, cookies;
cookies = readCookies();
if (!("style" in cookies)) {
    style = "basic";
    storeStyle(style);
} else {
    style = cookies.style;
}
will be sufficient. You can then use the style variable to load the appropriate style sheet.