I would do fusible applique for the large letters. If you have an embroidery machine, I would use it for the small letters. If you don't have an embroidery machine, I would mark the smaller letters onto the fabric and use a zig zag satin stitch to stitch out the letters following the outline.
I might mark the smaller letters on a separate strip of fabric matching the background and hand stitch it on after satin stitching the letters so it would be easier to manipulate while working on the letters.