It's always better to "couch" your grommets (cover them) ... what you lace with would depend on how much "support" you need - if the bodice is more decorative than supportive - then lighter (ribbons) could work. Personally, I've always had better luck with a thicker material (like modern shoestrings)

Many if not all lacing cords in period were make from cords made on a lucet. These are round or squared braided cords, basically made up in cotton, silk or wool.

You can find a machine make braid, usually in black but often in other colors, in fabric stores in their trim section or draperies that looks simliar to these, if you want to do that.

Shoelaces do work as well. I have used leather cord too. I think Michaels has this in packages but it's been a while since I've looked for it.

~Val

Not leather cord. It stretches and holds moisture, and without constant care will soon rot and break.
I use narrow satin ribbon in my bodies because it slides smoothly through the lacing holes. Your grommets would likely tear that to shreds, though. I'd say use bootlaces. They're long, sturdy, and cheap, so you can replace them when your grommets snag the laces and make them ratty. Couch the grommets if you want the whole thing to look a bit less glaringly modern, but remember that couching will reduce the size of your holes a bit, and friction from the lacing may wear through the threads over time.

Another option would be to place a guard over each side of the placket. Lay a strip of contrasting fabric as trim covering the holes, but just stitch down on the side of the holes away from the edge. Then you could still lace through the holes but they'd be hidden from view. If you can lace the whole thing closed, the lacing would disappear under the guards too.

P.S. If you're already wondering whether it's worth the effort to bother sprucing up a bodice that isn't going to be accurate anyway, you're mentally halfway to making a more historical garment next time to save effort and feel more enthused about your project. I'm telli'n ya, when you look up from a bunch of just-cut linen pieces and say, "Man, I'm gonna be so impressed with my smock! I can't wait to show it off to everybody!" , then you've been bitten by the historical clothing bug and may never ask, "Should I even bother?" again. It's a cool feeling.
Just sayin'

If you're close to making a new one, I wouldn't worry too much about going the extra mile, but you should couch/floss your grommets so they don't show.

For lacing, don't drive yourself crazy! Get a cotton bootlace and wax the bejeezus out of it so it won't break. You might want to cover the plastic ends with a simple metal point, or just make sure your ends are tucked in so they don't show.

When you make your next one, I recommend a fingerloop braid, but wax those fibers as you're weaving it, as well. The wax really makes it stronger & more durable.