What is the best format I can export or save a logo in for print and web?
I have created a logo in Illustrator.
In which file format / document settings should I save it so I can use it for creating a card in InDesign (print) and for placing it in a website?
For saving the file always use native file formats like EPS for Illustrator. That's for your file back up.
For print it is important that you use a
CMYK color mode. Now-a-days
EPS are used for printing. PDF is increasingly used now among designers. TIFF is used with ease since color management is possible but ask your printer if they accept TIFF.
For web logos use