You don't say whether you are doing hand, fusible or machine applique. If you are doing hand applique, definitely applique before making your quilt sandwich. If you are doing fusible, you can applique either before or when you make your quilt sandwich.
Whether you applique before or after you make your quilt sandwich, always outline the appliques as close as you can with a straight stitch. This will make your applique stand out from the background. IMHO, I would not quilt the letters, but would quilt around them. The denser you make the quilting around the letters, the more the letters will stand out.