It's not possible to make a general statement as to what is best, choosing fonts depends on how you intend to use them plus some personal preferences come into play, too.
My general preferences are like this:
I prefer system fonts for sites were text is dominant, the aesthetics are not so important and the priority is legibility. This would include forums, admin panels of business applications, documentations, specifications, large tabular data collections, source code, etc.
I choose custom fonts whenever their look is important for site design. Often choosing a good font can greatly increase the aesthetics of a web site and we may decide there's no substitute for a well chosen custom font. As for how to embed custom fonts I prefer to self host, however for quick effects I sometimes use google fonts.