I second what PrintDriver said. Always check the license, and just because you license the font doesn’t mean your client legally gets to. So if you package up native files for them, you may not legally be allowed to provide the fonts to them.
You also need to consider quality of the typeface and if it’s allowed to be embedded in a PDF for online use or printing. You don’t want to design something, get client approval, go to create a PDF and find out you can’t embed the font.
Unicode and OpenSource fonts are a good choice. Google Fonts are a good choice because then you can use them free and also use them across print and web.
I won’t use Typekit because when you cancel your Adobe subscription, they could potentially come after you, as you’re no longer licensing them at that time.