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My facsimile copy of the 1829 A. W. Kinsley & Co. specimen book shows only one option to fill your complete range of needs, and that is Bodoni: book, bold and ultra.

Didone fonts like Bodoni would be useful for text. Miller might also work well; Monticello might be still better.
Another display option would be an "antique" slab-serif. Something like Farao Black, maybe set in all caps, could work well.

Shinntype's Modern Suite is designed to produce a facsimile mid-19th century look. The bold caps of Figgins Sans are the only reasonably authentic style of sans, as sans lower case and other weights were not introduced until much later in the century, nonetheless the other Figgins Sans styles are based on the serif style of the era. Scotch Modern is a revival of what is probably a George Bruce (American typefounder) face in an 1870 Albany publication; however, the Scotch Modern style was widely used from early in the century.

Here is a sample of Scotch from 1815.

Miller does not correspond with this style of Scotch, in particular the capitals, shorter than the ascenders, and almost the same stem width as the lower case.

It depends on whether you wish to go with a Transitional style, such as Monticello or Miller, or the cool European modern (Bodoni), or a Scotch Modern. I would recommend the Scotch Modern, of course, the reason I revived it is because it does represent the 19th century in a way that Bodoni and the Scotch Romans (transitionals) don't, as it was the "default" American style for most of the 19th century, and those other faces were much used throughout the 20th century.