Pius XIII makes the most sense to me. Bl Pius IX issued the Syllabus of Errors, and called Vatican I, which in many ways is unfinished, as it was interrupted by the Franco-Prussian War and the attack on the Papal States. The war also served as a prelude to the horrors of World War I, the end and consequences of which Our Lady spoke of at Fatima; the quasi-pagan, secular nationalism and greed which caused the war, and the Marxism following the war were condemned by Pius, who would have been saddened at the course Europe took. Also, it is rightly called the Great War, and it set the 20th century on a collision course with the Church through the massive loss of life (modern arms industry was created), the political results, and the cultural shift it unleashed.
St Pius X focused on Modernism, which has infected the world very thoroughly. However, I remember him more for his role in the Liturgical Movement. He encouraged more frequent Communion, actual participation, and properly began simple reforms (not perfect to be sure). St Pius also assisted in the recovery of the chant tradition.
Venerable Pius XII engaged with the vicious unleashing of the two greatest systematic evils in history: Nazism/Fascism, and Communism. Pius also reached out to the people of the world, in an appropriate manner, in an attempt to show the world that it needed to catch the Church and not vice-versa.
We declare, say , define, and pronounce that it is absolutely necessary for the salvation of every human creature to be subject to the Roman Pontiff.Look how many people today promote pluralism in defense of the values stemming from post-Enlightened liberalism. Extra ecclesiam nulla salus [Outside the Church, there is no salvation] has virtually no meaning even to Catholics. Truth is now truths. Beauty is distorted in our choices of fashion, music, and art. Goodness is rejected for banal pleasures. I am not hoping for an archconservative Pope who will adopt an Ultramontanist position (which is not what Boniface VIII had in mind), nor a Pope more charismatic than Blessed Pope John Paul II who will reach out to the masses; it is 'both/and' rather than 'either/or' though, which really demonstrates how influential Benedict's pontificate is.
I seriously doubt it will be Peter, nor will a Peter be elected, in my view. The talk of Cardinal Turkson is just because of the 'prophesies' of St Malachy.
UPDATE: The commenter before me mentioned Pope St. Pius V, who I totally forgot about. He concluded the Council of Trent, and promulgated Quo Primum and with it the Missal of Trent in 1570. Now, this did kill some devotions that had layered the medieval liturgy and paraliturgical celebrations- in a good way, as it was very much centered on the Eucharist, following the doctrinal development of transubstantiation- but it did formalize the custom of praying the Prayers at the Foot of the Altar and reading the Last Gospel. The bull also highlights the importance of organic customs in the liturgical rites, thus preserving the Use of Sarum and the monastic rites, rather than innovation.