I have recently posted this answer that covers some aspects of the Italian unification process.

As for the specific reasons why the House of Savoy came to be favored over the others, one should observe that by mid XIX Century there weren't that many ruling Houses in italy with the power, prestige and degree of popular support (that is, at least somewhat appealing to the Italian "national" establishment).

There were in fact Houses of old nobility - a bunch of Hapsburg relatives, that had been suggested in hopes to find acceptance with the Austrians, but the last "serious" candidate had been Francesco IV of Modena (who was incidentally the brother in law of future King Victor Emmanuel II); and by serious I mean that he at least had thought of it. An Austrian King would not have ruled over Italy anyways; more over a central Italy federation built in opposition to the Piedmontese and the Neapolitan.

The Kingdom of Naples had no interest over the unification of Italy, being afflicted by mid XIX by a deep internal crisis, in full display after the King Ferdinand II of Bourbon had shifted progressively towards an authoritarian and absolute rule after the failed revolution of 1848-49. By this time, not even the Neapolitan establishment was so fond of their King.

A third possibility (and again, one that did not include the Piedmontese state in a possible expanded kingdom) was the return of a Napoleonid ruler - that is one of the many relatives and descendants of the old Emperor and "honorary" President of a few Italian republics during the 1801-12. But that again was more of a quirk of some Italian conspirators, knowing that the name Bonaparte had still an evocative sound.

Overall, an Italian unified kingdom could only be formed with a certain degree of strength, both military and diplomatic; and - as explained by Massimo D'Azeglio in his political tour of central Italy - the only one with both was the King of Savoy, Charles Albert at that point; who had strongly disappointed the Italian patriots around twenty years before with his uncertain conduct during the national movements of 1821 (when he was still just the Prince of Carignano), but appeared up to his abdication after the defeat of the First Independence War the most viable candidate.

More so, the Piedmontese Kingdom was a rather solid and stable political formation, to the point where one of the conflict element during the unification was the tendency of certain portions of the ruling establishment (notably the "French" ones) to envision a Piedmontese expansion rather than an Italian unification - the contrast between a Piedmontese and an Italian view of the unification process.

It is fair to say that, despite the defeat of 1848-49 (one that had forced Charles Albert to abdicate in order to save the dynastic continuity of the Piedmontese State) by the late 1850s the unitarian tendency was the predominant one; nonetheless, even the most direct agents of the unification like Piedmontese Prime Minister, the Count of Cavour, had originally envisioned a Kingdom of (Northern) Italy with the inclusion of Tuscany, the Austrian Ducates, Milan and perhaps the Papal Legations.