1. Cut all the bodice pieces in all four fabrics.
2. Baste the fashion fabric pieces to their corresponding cotton pieces, wrong sides together. Then baste the lining and strength layer pieces together in the same way. You're not sewing seams at this point, you're just sewing layers together so you'll end up with half as many pieces. The lining/strength layer pieces will form an "inner half" of the corset, the bones will lie in the middle, and the fashion fabric/cotton pieces will form the "outer layer". Baste by machine - just sew with the biggest stitch you can, just outside the stitching line.
3. Now there are just a few more pieces to cut. These will form the lapels and chemise-like laced centre front section.
Baste the cotton pieces to the secondary fabric pieces. The "lapel" lining pieces will stay as one layer.
Now you should have two complete sets of bodice pieces - one set in fashion fabric backed with cotton, and one set in your strong fabric backed in lining. You should also have two front pieces in your "secondary" fabric backed in cotton, plus two front pieces cut out of skirt lining.
Set aside all except your set of strength layer pieces. You need to bone these. Yes, as you can see above, I used Rigilene - it's light and I needed lots of it, and it's easy to sew directly onto the fabric and cut with scissors when you get close to the edge. Use your basting lines as a guide, with the boning starting and ending 1/8" (1/4cm) inside the stitching lines.
For a more period accurate look, don't use steel - it's no more accurate for the 1660s than Rigilene and you'll never be able to lift the resulting bodice (although I suspect it may be bulletproof). Use reeds. They're cheap and you can get them at www.corsetmaking.com or Vena Cava in the UK. To use them, you'll need one more extra layer of fabric. You'll need to make boning channels first by placing the new pieces of fabric over the strength layer/lining, sewing boning channels and then stuffing bunches of reeds in the gaps.
In either case, note that you can bone the pieces before joining them together, which makes things a lot more manageable.
NB. You won't be able to make boning channels by the "sandwich" method (sewing the layers together, stitching channels through all layers and then inserting bones) because you'll get in a mess with the lapels and front edges.
So now that you have your inner strength layer pieces boned - the back, sides and fronts - we can move on to make the front section pretty!