Hertzl leaned socialist (he talked about a "third way" but we know from Blair and Clinton that that's just code for liberal-socialism)...those who came after him were more hard-core.
Herzl's novel was entitled Altneuland (tr. "Old New Land") and famously presented a utopian Jewish state that didn't seem in the least bit Jewish (as I said, he was secular). He saw it operating on a system he called "mutualism," which may not be capitalism but isn't socialism either (some anti-capitalist right wingers advocate things like mutualism, communitarianism, agrarianism, and distributism).
Herzl's idea was a Jewish home for Jews in the ancient land. His utopian novel was a silly and enthusiastic picture of what this future state would be like, but there was absolutely nothing practical about it. Furthermore it wasn't socialism as it had always been practiced and advocated. That came later, during the Second `Aliyah.
Much of Herzl's initial support actually came from Orthodox Jews in eastern Europe. After his death the socialists came to dominate, and their Marxism and hostility to Judaism turned most Orthodox Jews against Zionism for some time.
I reiterate: Herzl was secular, but not a socialist. His utopian novel had very little, if anything, to do with the actual work of the early Zionist Organization. The socialists of the Second `Aliyah came to dominate Zionism after Herzl's death.
There were even fascist Zionists for a little while in the early Thirties, you know.
These beliefs would not be held by the "right-wingers" associated with conservatism today and would be considered socialist, for example, on FR.
I believe that these beliefs would fall more into the "Clinton-Blair" mold which if adopted leads to more and more State control (as happened after Herzl I might add).
No suprise. These were the poorer Jews, many of whom were attracted to the socialist and communist mindset.