See if you can get "Goudy Cursive" as well, which was a set of swashes for Goudy Oldstyle italic.

Great suggestion! I was not aware of that option.

Just a note: although all these designs carry the name 'Goudy', they were not designed as a 'family'.

Here is a full list of Goudy's eponymous types, as listed in the index of Goudy's Type Designs (2nd Edition, New Rochelle, 1978), which is a facsimile edition of the original two Typophiles chap books (XIII and XIV, 1946).

Goudy Antique
Goudy Bold Face
Goudy Book
Goudy Cursive
Goudy Dutch
Goudy Heavy Face
Goudy Heavy Face Italic
Goudy Italic
Goudy Lanston
Goudy Modern
Goudy Modern Italic
Goudy Newstyle
Goudy Old Style
Goudy Old Style Italic
Goudy Open
Goudy Roman
Goudy Stout
Goudy Text
Goudy "Thirty"
Goudy Uncials
Goudytype

Only some of these were designed in coordinated styles, intended to form part of a family.

Goudy appears to have referred to his Sans, simply as 'Sans Serif'.

His proprietary types for the Saks department store are listed as
Saks Goudy
Saks Goudy Italic
Saks Goudy Bold

Two sources for Goudy stuff are Lanston Type Company, part of P22, and I see that at Goudyfonts there are links to many fonts—though some of their links are broken. Steve Matteson has revived some Goudy fonts; you can see the links here. And Font Bureau's Californian has had various hands reviving its weights, including Carol Twombly and David Berlow. And Berlow did Goudy's Village. Tony Stan's ITC Berkeley us another, softer take on Goudy's California Old Style.

Lanston's Goudy Old Style has the option of the original full descenders, which is nice. I think Typophiler Paul Hunt had a hand in the Lanston Goudy revivals, but I'm not sure. The Font Bureau's versions have tons of weights and styles.

The quality varies at lot—including among Goudy's originals!— so sorting through these will take a while. I haven't done it.

Wow. Incredible responses. Far more than I anticipated.

@John Hudson: Have you ever worked with Goudy Sans? Can you recommend a version that pairs?

I've worked with very few Goudy types. I'm not a fan. I admire Scripps College Old Style, and to a lesser extent Californian, but that's about it. This isn't to say that I don't recognise his importance or understand why some of my colleagues are such big fans. And I do appreciate Goudy's insistence on controlling the production process, of not only designing but cutting and casting his own type. In this respect he is the fore-runner of all of us who make our own digital fonts. But most of Goudy's types are not to my taste.

I think I remember Erik Spiekermann, who I think likes Goudy, saying that Goudy Sans is 'over designed'. By that I think he means that it is so assertive and has so much personality and individual quirks that its use is restricted. Personally, I think it can look great in some settings by itself, but I'm skeptical about it 'playing well with others.' Because of the slanted crossbar on the e, you might try some of Goudy's many faces with slanted crossbars on the e, such as Deepdene.

Back to the original, sans aside—I’ll have to look into that a but more—suggestions as to a single family that strikes the best balance between size of family and authenticity?

I recently inherited a case of original lead Goudy Thirty. It is gorgeous. A wonderful, lyrical sort of cross between a blackletter and a roman.

And of course there are others, like Deepdene (maybe my favorite) that are not eponymous, but these certainly weren't meant as part of the "Goudy family."

Richard Beatty has done digitizations of a couple of Goudy’s typefaces, most of which have small caps, swash letters and alternate figure sets:

Goudy Claremont
Goudy Italian
Goudy Mediaeval
Goudy Saks
Kennerley
University Old Style

Disclaimer: I produced the OpenType versions for Richard.