Paul Preston's The Spanish Holocaust is an excellent book on the subject. In it, he argues that the Nationalists engaged in a deliberate campaign of violence against noncombatants. I find his arguments to be persuasive, despite a few flaws in the book. His pro-Republican bias shines through too often for my tastes, but readers can account for that. I think his argument that the White Terror constitutes a "holocaust" to be overstated. However, his research is immaculate. It is the best English-language coverage of the subject of violence against noncombatants during the Spanish Civil War.

The book is replete with documented incidents. When Nationalists took over an area there were immediate and ongoing purges and arrests. You could be killed or imprisoned for any number of offenses, both real and imagined. Among the targeted groups were politicians of the previously elected regime (regardless of how they acted prior to the uprising or after it), union members of any kind, members of leftist political parties, journalists, doctors, women (rape was also common), anyone suspected of joining or supporting the Republican faction, and others. Prisoners of war were mistreated and sometimes killed, such as when POW's were machine-gunned in the massacre of Badajoz. One could be executed immediately after falling into Nationalists hands, or later--days, weeks, or months. Sometimes this happened after a short "trial," procedures that were mockeries of the term. The defendants were not given anything close to an adequate defense, the evidence produced for their "crimes" was most often flimsy or manufactured, and groups were sentenced to death--sometimes without even comprehending what they were being charged with. To call these executions a travesty or a tragedy would be a massive understatement.

The Nationalist campaign of violence against noncombatants was deliberate and ongoing, resulted in the deaths of tens of thousands of people (Preston estimates 200,000), and were often criminal in nature.

Here is another incident of violence against noncombatants that I find disturbing, a section of Preston's book regarding the "Caravan of Death"--a retreat of citizens from Malaga to Almería. (The Spanish Holocaust, pg 177-8)

Warning The below passage is graphic in nature.

Even before the occupiers began the executions [in Malaga], tens of thousands of terrified refugees fled via the only possible escape route, the 109 miles along the coast road to Almería. Their flight was spontaneous and they had no military protection. They were shelled from the sea by the guns of the warships Cervera and Baleares, bombed from the air and then machine-gunned by the persuing Italian units. The scale of the repression inside the fallen city explained why they were ready to run the gauntlet. Along the roughly surfaced road, littered with corpses and the wounded, terrified people trudged, without food or water. Dead mothers were seen, their babies still suckling at their breasts. There were children dead and others lost in the confusion as their many families frantically tried to find them.

The reports of numerous eyewitnesses, including Lawrence Fernsworth, the correspondent for The Times, made it impossible for rebel supporters to deny one of the most horrendous atrocities perpetrated against Republican civilians. It has been calculated that there were more than 100,000 on the road, some with nothing, others carrying kitchen utensils and bedding. It is impossible to know accurately but the death toll seems to have been over three thousand. The Canadian doctor Norman Bethune, his assistant Hazen Size and his English driver, the future novelist T.C. Worsley, shuttled back and forth day and night for three days, carrying as many as they could. Bethune described old people giving up and lying down by the roadside to die and ‘children without shoes, their feet swollen to twice their size crying helplessly from pain, hunger, and fatigue.’ Worsley wrote harrowingly of what he saw:

The refugees still filled the road and the further we got the worse was their condition. A few of them were wearing rubber shoes, but most feet were bound with rags, many were bare, nearly all were bleeding. There were seventy miles of people desperate with hunger and exhaustion and still the streams showed no signs of diminishing … We decided to fill the lorry with kids. Instantly we were the centre of a mob of raving shouting people, entreating and begging, at this sudden miraculous apparition. The scene was fantastic, of the shouting faces of the women holding up naked babies above their heads, pleading, crying and sobbing with gratitude or disappointment.

Their arrival brought horror and confusion to Almería. It was also greeted by a major bombing raid which deliberately targeted the centre of the town where the exhausted refugees thronged the streets. The bombing of the refugees on the road and in the streets of Almería was a symbol of what ‘liberation’ by the rebels really meant.

Taken as a whole, Nationalist violence against noncombatants was widespread and deliberate. It included targeting individuals for their political beliefs, but it also included attacks on suspected "leftists" without any real evidence as well as killings of suspected Jews (despite the fact that the actual Jewish population of Spain was tiny). There were also general bombardments of civilians such as the above attack near Almería and the infamous bombing of Guernica. Tens of thousands were killed, many were buried in unmarked graves, and many families never found out the actual fate of their loved ones. The White Terror in Spain during the Spanish Civil War was brutal, barbarous, and sickening.

I hope that answers most of your question. As always, followup questions from OP and others are encouraged. Preston's book is the book on the subject if anyone is interested in reading more.