Based on the Preface, Introduction and chapters 1-4 of Ian Haney López's Dog Whistle Politics: How Coded Racial Appeals Have Reinvented Racism and Wrecked the Middle Class What type of Republican was Goldwater? How did he view race? Why did he lose the 1964 presidential election?

The answer to this question can be found in Dog Whistle Politics' first chapter, "The GOP's Rise as 'the White Man's Party.'" Barry Goldwater was a Republican who, like George Wallace, saw the opportunity to harness the racist hostilities of the South to power his political ambitions. His political maneuvering as an Arizona senator helped drive the Republican Party to the far right, contributing to its transformation into the aforementioned "White Man's Party." 
As López asserts in this chapter, Goldwater was "a walking embodiment of the Marlboro Man's disdain for the nanny state," while at the same time voting in favor of federal civil rights legislation in 1957 and 1960. His attitudes toward race quickly turned in 1961, when he realized that it was more beneficial to his career to "go hunting where the ducks are"; he began to leverage the division in racial politics of the parties, voting against the 1964 Civil Rights Act (which was otherwise supported by 90% of non-Southern senators) and claiming that he did so to protect "states' rights" and "freedom of association." 
Gaining steam, Goldwater decided to run for president in 1964 and used Wallace's "soft porn racism" techniques to further his campaign. Goldwater led a particularly theatrical campaign in the South, pandering to their racist sensibilities with a tableau of "seven hundred Alabama girls in long white gowns" and "a great field of white lilies" flanking the floor of the football stadium in Montgomery where he was to give a speech. Goldwater's mistake, however, was in railing against the New Deal, which had proved to be very popular in the South after the Great Depression had economically drained the region. This, combined with the fact that Goldwater was a Republican--a party which the South associated with Lincoln, the Confederate's loss in the Civil War, and the fight against segregation in schools--lost him some Southern votes.
Still, Goldwater did manage to pull through in the South. It was ultimately Goldwater's anti-welfare obsession that cost him the presidency, with voters outside of the South (in every state except Arizona) voting against him. Goldwater's foreign policy and militarism certainly didn't make him a more attractive candidate either. Thus, ended the "big-money/small-government conservatism" of the era with progressive governance rising to power.