For a banner of this size quilting is not strictly necessary. However some quilting just around the motifs of the embroidery can enhance the look of them. I would suggest doing the embroidery first - probably with an extra layer of muslin underneath if parts of it are going to be densely stitched. All banners I have seen do not have quilting detail showing through to the back lining. Then construct the layers, this can be done at least 2 ways that I can think of,
1) mostly hand work - lay out the 'top' face down on a table, cut your stabiliser/batting to finished size and place in position. Th top needs to be a good 1.5 inches larger all around (more is good). Fold in the edges, pin,then herringbone stitch in place. Mitre fold the corners. then take your backing/lining, centre it up, fold in the seam allowances so that they are just short of the edge (1/16"-1/8"), pin from the centres to the corners and work from opposite sides evenly so that it is laying flat. Stitch together, using slip stitch or ladder stitch. If doing it this way, you could incorporate a hanging sleeve under the lining.
2) Mostly machine work - Lay out the backing right side up. Lay out the 'top' right side down on top of it. lay out the stabiliser/batting on top of the 'top' smoothing as you go. Pin it together around the edges. Machine together leaving a 6"-8"gap (at the top would be least noticeable in this case). Trim the batting only close to the stitching line. Fold the corners neatly and turn it through, 'roll' the edges between your fingers, so that they are neat & the seam is on the edge - you could press it at this stage. Machine edge stitch it all the way around. The sort out your hanging sleeve.
If the banner is going to be hung by tabs these will need to be added before the lining is stitched into place.
Hope you show us the finished piece