I have recently completed an 1860's corset, made from many layers of linen which I had leftover from making 18th century shirts and shifts.
In the mid-19th century manner, I did use a sewing machine. I live near Washington DC, so in my interpretation of a senator's wife living in the federal city, a sewing machine usage is highly plausible I would think. I read lots of reenactor's forums and repeatedly I read that corsets of this era are not meant to squeeze you like Scarlett O'Hara and Mammy would make one think! Instead they help to shape the body into the hourglass shape, but not to the extreme of squeezing the body.
For the outer layer I purchased some linen with a damask print.
Then like many extant corsets with lace, I handsewed cotton lace from my stash to the edges. I already had a package of grommets in my stash, so no new purchase needed there.