Let me start out by saying that I am not a big fan of "designer gods". You probably know the kind I mean: the ones with the five syllable, non-English sounding names, obscure powers and identities, strange motivations... i.e., the one's that are everywhere homebrewed by imaginative DMs and make appearances in many commercial modules. These "designer gods" seem to abound, spreading in numbers that seem to me, to be unjustified.
I think a quality campaign is served well when the structure of the supernatural is intuitive, and simple for any new player to jump into. Most gods can serviceably go without any personal name. This also goes well with the idea of a Dawn of Civ campaign. It gives it a certain "primitive" feel, when the gods are simply referred to as "the Thunderer", "the Fire Starter", "the Sun Bearer", "the Tempest Bringer", "the All-Mother", that kind of thing.
Which pantheon are they? Well, it hardly matters, really, when they are broken down to their primitive, pre-literature level. The operating assumption in the ancient world was SYNCRETISM, the idea that, although we have our own particular names for them in our own languages, the gods behind these forces are one.
Gods as Forces of Nature
The "look and feel" I am going for here deviates strongly from our civilized view of pagan gods, that comes from our literary encounter with the Greek/Roman pantheon. I am going for something more along the lines of the gods in Niven & Pournelle's Burning City books (the Magic Goes Away series). These gods are primitive, scary, and very much out of control.
For example, the Burning City's god of fire, who inspires arsonist orgies of destructive conflagration at random intervals, yet prevents the use of any indoor fires in normal times. Drawing from real history, it is like the ancient festivals of Bacchus, where we get drunken orgies, people running around out-of-control because they are possessed by this god of lust and pleasure.
Imagine a primitive town, a la the Burning City, except, rather than ruled by a fire god, is under the control of the Goddess of Love. Under normal circumstances, fighting or sex is impossible there. Literally, people find it impossible to draw arms on each other, or come to blows, or engage in any sexual activity.
Yet a couple times every year, the Goddess goes into her active phase, and everyone suddenly goes crazy, screaming, yelling, pushing, fighting, ripping their clothes off, making love in the street, that kind of thing. [I am thinking the town of this goddess is a thriving merchant town with a, ehem, "wild side"... hmmm, Scottsdale perhaps?]
THAT would be a very different city in concept and application than the standard "medieval European" milieu we are used to, wouldn't it? This gets us back to that primitive idea that each city has their own patron god/goddess. It's not so much that people are picking and choosing their own personal belief system, which is our modern idea of religion. The idea is that a god is in control of a certain region, and the humans who live in that region are under the control and protection of that god.
Evil Gods vs Demons
I am also not a fan of "evil gods". I think this role is better filled by demons and devils. Evil clerics are those who have made deals with these evil creatures. The dark forces agree to reward these clerics with miraculous powers in exchange for serving them, or selling their souls to them, that kind of thing. Of course, serving evil is unpredictable, dangerous, and always has a high price. Their activities are done in secret, and usually their identity as evil clerics is hidden from the public eye as well.
The Mechanics of Cleric Power
Clerics are miracle workers. I think their mechanics have been improperly conflated with that of magic users, because of the "spell slots" structure. I am fine with limiting clerics to their allotted number of "spells" as per the slots, but I disagree with the idea of preparing them ahead of time.
Miracles are, by their nature, ad hoc, as needed. Thus, a 1st level cleric could call upon their god once a day for a low level miracle (i.e., one first level spell slot). Which miracle that is, is up to the cleric at the moment of need, and can be drawn from any of the potential first level cleric spells.
Supernatural Embedded in the Material
As you can infer from my discussion of the fire god or love goddess above, I disagree with the abstract idea that gods are far removed in some other plane of existence. Returning to the primitive ideal, gods have specific locations on earth, like that mountain, that volcano, deep in that canyon, at the roots of that tree, etc. These are places of temples, pilgrimages, even towns that develop, devoted to those specific gods. Their power is not necessarily transferable to other locations, i.e., they would be a poor fit for an adventuring cleric. Adventuring clerics might even find their miracles restricted in these zones (although they would not know that ahead of time, of course)...
Some gods are above, in the literal sense of above, meaning, in the clouds, in the sun, in the moon, in the stars, in the planets (where are embedded in the dome of the sky, not in some infinite space like our modern scientific view). These gods tend to be accessed only from the highest mountain peak, or some means of flying upward. Because these gods can see the whole earth, their worshippers are more mobile, and thus, would be more appropriate for adventuring clerics. Do their powers extend underground, and if so, how far??? That would be a fun plot twist to explore, as your cleric, a devotee of the Thunderer, finds his miraculous powers fading as he progresses underground....