CSS linked SVG search icon

I’ve been trying to make a custom search icon rather than the the ugly square box for my website, and want to do this via an svg that is customizable in the css. I’ve delved into the PHP but may have bit off more than I can chew trying to insert the SVG reference. The file is slightly different from the default being a premium theme but is close enough where the small differences appear to be inconsequential:

<form method="get" id="searchform" action="<?php echo home_url(); ?>/">
	<input type="text" value="<?php _e('Search','revoke'); ?>" onclick="value=''" name="s" id="s" />
	<input type="subtmit" id="searchsubmit" value="<?php _e('Search','revoke'); ?>" />
</form>

I know that I should be inserting the image in the third line, but replacing it with an SVG with an ID linked to the CSS (maybe still retaining #searchsubmit) while still allowing it’s search form functionality is beyond my slightly better than basic understanding of PHP. Anyone know a good solution?