help with custom search box

Hiya,
Not sure if you can help with this or not, but I’m building a public library website, so I needed a search that would search both our catalog and the website. Our IT guy gave me this code based on what we have on our current website (mesacountylibraries.org) and I just don’t know where to put it exactly…I’d like the search box to be here somewhere:
http://screencast.com/t/g6HbqPFAINaP

Should I use a text header widget? Put it in the header file (masthead.php)? If the theme updates, will I lose the code if I put it there? Also, I’m assuming any styles I apply need to be put in the custom CSS section?
TIA!
code he gave me:

<form id="searchform" onsubmit="return false;" name="searchform">
    <input placeholder="Keywords" id="lookfor" name="searchterms" size="25" type="text">
    <input id="searchbutton" name="submit" value="Search" type="button"
    onclick="var sf=document.searchform,l=sf.sengines.length-1;for (i=l;i>-1;i--){if(sf.sengines[i].checked){var submitTo=sf.sengines[i].value+escape(sf.searchterms.value)}}window.open(submitTo);return false;">
    <div class="search-options-header">
    <label><input name="sengines" value="http://mesa.marmot.org/Union/Search?searchSource=local&basicType=Keyword&genealogyType=GenealogyKeyword&lookfor=" class="input-header" checked="checked" type="radio">Catalog</label>
    <label><input name="sengines" value="http://mesacountylibraries.org/?s=" class="input-header" type="radio">Site</label>
    </div>
</form>

URL: http://caritaylor.com