My client has asked for their logo files, (the source file is vector AI created with Illustrator). He wants a file for the web/printing letterhead (online and paper invoices) and a vector file for the printing materials like marketing stuff and advertising (t-shirt, trifold, stickers and business cards ...). What’s the best way to convert the original colours without changing them or ending up with a bad colour final result?
Generally speaking, use RGB for web, and home/office inkjet printing (with sRGB as the profile).
CMYK for professional digital/lithographic printing, or even Spot Pantone colours for lithographic printing/screen printing.
Some formats to give your client: Vector: PDF, SVG, EPS, and Raster: PNG, JPEG, CMYK TIFF. That should just about cover everything they will ever need.