[noun] + が + 何より + [i-adj / na-adj] 何より + [sentence] [verb て-form] + 何よりだ [noun / na-adj] + で + 何よりだ
何より means "more than anything": it marks one thing as the most important or the best. It goes in front of the adjective or verb it strengthens.
なん何よりも adds も and means the same, a shade stronger.At the end of a sentence, 何よりです is "that's the best thing", which in practice means "I'm so glad". It follows a て-form, or で after a noun or な-adjective, and it is the warm, polite thing to say on hearing someone's good news.
It works for your own side as well, when something turned out better than feared.