Using only fonts from Adobe will ensure that users can sync the fonts used in MOGRTs to their own system automatically. Your customers will never need to install fonts manually, and they will never complain about not having the right font.
Most fonts from Adobe must be licensed and paid for, though—and your client will probably not want to pay extra for fonts to be able to use your MOGRTs.
Edit 2020/07/09: Since I wrote this article, Adobe has released most of the fonts ad fonts.adobe.com for free! So now you have a much wider choice of fonts.
Also note that Bebas Neue has been removed from Adobe fonts, which can cause some problems for older MOGRTs that used this font.
The fonts below from Adobe can be used for free by everyone who has a Creative Cloud subscription. This makes them perfect for Motion Graphics designers who make MOGRTs.
(The screen grabs were made October 6th 2018.)