"And by that I mean I am interested in the religious history, as I find it all fascinating...."
Jerusalem and other parts of Israel are fascinating for those with an interest in history, particularly archaeology related to religious historical sites.
Given that you're "not religious but are interested in religious history", you'll probably want to start your research by Googling sites that say "Israel" rather than "Holy Land."
Jerusalem would be an obvious place to focus your research, since it has key historical sites of three religions: Judaism, Muslim/Islam, and Christianity.
If possible, try to sleep in the Old City rather than the rest of Jerusalem, or at least within easy walking distance of the Old City. In previous visits I've found it possible to sleep in the Old City, such as a French-based convent that is specifically set up to provide accommodations for Christian pilgrims (the nuns were young Arab Christian women). You don't have to be a particular religion to stay there.
The "newer" cities, such as Tel Aviv, will have limited historical sites.
The Galilee area has sites mostly associated with places where Jesus lived and preached, which may be of great interest even to those self-described as "not religious." Notable among these Galilee locations is the village of Kefar-Nahum (Capernaum in the Christian Bible) at the north end of the Sea of Galilee (which is really a lake) and the site of the Sermon on the Mount (not the exact spot but close and inspirational even if you're not particularly religious).
Masada also comes to mind, but you will want to do a day-tour there from Jerusalem.
In general, Israeli drivers are known as fairly assertive, which might be just another reason you would want to avoid renting a car. And definitely don't do rental car in any city.
With sufficient research (which it seems from your post that you would be inclined to do), you can rather easily DIY in the Old City and walk everywhere. No need for tours there, it's a small geographical area, even sites outside the Old City walls, are relatively easy to walk to or a short taxi ride away, places such as the Mount of Olives, Pool of Siloam, Kidron Valley.
Outside of Jerusalem, you can see a variety of historical sites associated with Judaism, what religious Christians would tend to think of as "Old Testament" (aka The Hebrew Bible). Numerous sources of information (internet and books) will give you plenty of information on these other locations.
A long-time member of this forum is Chani from Tel Aviv, you might want to use the Private Message feature of this forum to contact her.