Trying to display terms from custom taxonomy within function

Function get_term_by returns object or array (based on $output arg) on success and false if failed. But you treat it as string and try to concatenate it. So your code should be following:

$cat = get_term_by('id', 17, 'project_cats');

$html_content .= "<h3>" . rgpost('input_1') . "</h3>"; //Title
$html_content .= "<p><strong>Category:</strong> " . rgpost('input_5') . " | <strong>Budget:</strong> " . rgpost('input_3') . "</p>"; //Category & Budget
$html_content .= "<p>" . rgpost('input_4') . "</p>"; //Description
$html_content .= $cat->name;

Read more about this function in codex.