There were many bases of support for the Nationalist cause. A simplified list would include the military, industrial and agricultural businesses, monarchists, the Catholic Church, and military aid from Mussolini's Italy and Hitler's Germany. Starting with the military, there were a number of generals besides Franco, each with their own bases of support and agendas. Generals Mola, Goded, and Sanjurjo were all rivals of Franco within the military. Sanjurjo died in a plane crash at the outset of the war. Goded was captured early on and was executed. Mola also died in a plane crash later in the war. Primo de Rivera was in Republican custody and was executed by the Republicans as well. His heir in the Falange was brought under Franco's control and was later sidelined. Gil Robles--previously the leader of the CEDA--faded into the background. The same went for the Carlist and Alfonsist leaders and claimants. In the end, Franco was able to subsume all of these groups into his own.

The Carlists and Alfonsists had dreams of restoring the monarchy (under two different claimants). The Falangists wanted to create a fascist state. Many Catholics wanted to resist the left's attempts to secularize the country. The military wanted to reclaim some glory as well as resist reform measures that would have reduced the size of their institution. Industrialists wanted to avoid their workers unionizing or even being collectivized, and the same could be said for large agricultural interests. Others just wanted power, as you mention. That Franco was able to make all of these interest groups fight the Republicans rather than each other is his main accomplishment in the war, in my opinion. For all his many faults, he was able to carve a path that led to himself taking power while sidelining his rivals--all while creating an organization that would also defeat the Republicans. Franco also was able to secure that the foreign military aid he received (notably from Italy and Germany) did not come at a cost of losing control of his faction--or at least he was better able to pull off this feat than the Republicans with their outside aid.

If things had gone differently, a fractured Nationalist cause is easy to imagine given the lack of a coherent philosophical core. As it played out, Franco was able to position himself to be the beneficiary of the squabbles within his faction while avoiding internecine fighting. In the end, all of the factions under the Nationalist banner were subsumed by Franco.

(edited to add) For this particular question, I would suggest Beevor's The Battle for Spain for the military side of things. Thomas and Preston (both titled The Spanish Civil War) cover the ideological aspects admirably. This topic has a whole lot to wrap your head around--my answer is at best a radical simplification.

Also I will include a disclaimer on Franco. While his political maneuvering in this arena is praised by my post, do not think that I am any fan of Franco. His regime was murderous, and I like Sanchez' description of his rule as "barbarous". For a thorough breakdown of the Nationalists' crimes the best source is Preston's The Spanish Holocaust (while the title can be debated, the scholarship and research found within the book is incontrovertible).