I’m going to adjust your question somewhat and separate some of your attributes. In terms of wealth, I would hazard a guess that its greatest period of wealth is today. Its Institute for the Works Religion—the so-called “Vatican Bank”—is [worth about 8 billion] (http://www.ibtimes.co.uk/pope-franciss-church-poor-has-assets-worth-billions-1457383). That’s not counting its property holdings across the world or its artworks. (This doesn’t mean the bank can’t run deficits, as it did in 2011 when income from Catholics was smaller than expenditures. Also note that the artworks are “priceless”—unlikely to be sold anytime soon at any cost.)

In terms of power (and I think I can say territory, at least indirectly), its zenith was the papacy of Pope Innocent III (1198-1216). By virtue of his theory that the church could intervene in secular matters when they touched on matters of sin (“ratione peccati”), he intervened in King John’s selection of the Archbishop of Canterbury. When John resisted, he excommunicated him and put England under interdict. When John finally conceded, part of his settlement was to make England a fiefdom of the papacy. It’s this power over the English crown that, for instance, caused Innocent to side with John over his barons when they forced his signature on the Magna Carta. (And let’s note its 800th anniversary now being celebrated.) He likewise intervened in French politics and in the selection of the Holy Roman Emperor, which also gave him influence of its kingdom of Sicily. So while he wasn’t successful in claiming land lost from the Papal States of central Italy, he successfully claimed limited authority over the governments of England, France, and other countries. He launched a crusade against the Cathar heretics in southern France and, more importantly, the aborted Fourth Crusade which diverted to Constantinople, captured the city, and briefly reunited it with the Catholic west. He called the very influential Fourth Lateran Council in 1215, which laid down regulations for the running of the Christian church that were in place for several centuries. I’m hard pressed to think of another pope whose influence affected so many political and spiritual policies.

(Source: for a brief history see Eamon Duffy, Saints and Sinners [1997]. A much more nuanced view than I’ve summarized here is John C. Moore, Innocent III (1160/61-1216): To Root Up and to Plant [2003]).