Nook, not Kindle, for the following ymmv.
I convert using calibre. It works, and works quite well for most things. It is also free. Kindle's format is one of the conversions it will make. (I don't know rules about linking to various products so I'll let you browse/datasearch (a low threshold test) instead.)
PDFs are the hardest formats to convert, regardless of program that's doing the conversion. You'll have to tweak to make it work (which it sometimes will not). The good news is that the providers suggest tweaks, and those usually work.
Obviously I've not used Kindle's Personal Documents, but I see no reason to expect them to be worse than Calibre. That means it should make at least decent conversions.