A logo script must survive every size from a favicon to a shopfront, so the priorities are stroke weight, distinctive capitals and clean joins. Pacifico, Lobster and Sacramento reproduce reliably; Great Vibes and Allura suit premium and bridal brands; Dancing Script and Cookie read as warm and approachable.
Checks before you commit
Read the wordmark at favicon size, in one colour, reversed out of a dark background and mirrored, since all four happen to a logo eventually. Bold and monoline scripts pass those tests; hairline scripts fail the first two. Export the SVG for the designer, who will convert the letters to outlines and adjust the spacing by hand; the OTF export gives the brand kit a small font holding just the letters of the name. Keep a black-on-white master. The fonts are free for commercial use, but a font is not a trademark: if the wordmark will identify a business, the usual trademark search still applies to the name and the mark as a whole.