A few things.
First, if we want a permanently manned lunar base like the ISS, nuclear power is really the only viable solution.
Second, Solar is fine for more of an “outpost” that’s not continuously manned. An outpost with a few hab modules, solar arrays, rovers and equipment, that we’d do 2-week long missions to would be fine, and probably a logical first step. Pick a nice, interesting location, drop a couple of cargo landers there with hab modules, a pressurized rover, and solar arrays, then send humans there to set it up, and then use that as the site for X number of future missions for 2-week says. A good and simple first step.
Third, the polar base theory. Here’s the thing, there’s certain locations at the South Pole at least with crater mountain peaks that are exposed to sunlight –most- of the time. There’s no proof yet of a “Peak of Eternal Light”. But good prospects for peaks of light 70-80% of the time. However, a big problem is how do you get these big, ISS-type solar arrays up to the top of that peak, especially if it’s jagged and steep? You can’t just get it –near- the top, you need it right at the peak so it can track the sun. If it’s on the slope, the sun will go behind the peak for ½ the lunar day, and you are right back to where you would be if you were at the equator. And what if the peak is rocky and jagged (likely), how do you climb it and set up this huge array in a space suit? Maybe a long way down the road, but that seems like a pretty tall order. People seem to think this would be easy, but the only places even at the pole that would have light most of the time are the peaks.
Probably, you’d need at least 2 or 3 redundant arrays located on different high slopes facing in different directions if there was such a location at the pole so that at least one array would have sunlight at all times. But you are talking a lot of power cables to go from these hill and mountain tops to your base. That’s weight, and weight costs money.
So in short, I think at first, a few outposts at various interesting locations on the surface (including the south pole) that would be manned for 14 days at a time solar powered would be a logical first step. (plus you reuse that equipment for several missions which helps save costs too rather than throwing it away each mission) And once you’ve done that and learned much more about living on the lunar surface, you pick a place for a permanent ISS style base, and you almost assuredly make that nuclear powered. Perhaps after that, we could change the structure of lunar missions. Rather than space based missions, they would be staged from that base. Regular cargo landers would land there with supplies and fuel. A reusable crew lander could be used to ferry crews to and from orbit. (you could use a reusable cargo lander too maybe, but transferring cargo in orbit might be a problem), and then you have a surface-to-surface ship that launches from the base, goes sub-orbital and lands at an interesting location. It’d carry a rover, supplies, equipment, and enough fuel to get back to the base.
Another possibility, with all the power a nuclear plant to generate, for fuel, you could transport water to the surface (don’t need to have it pressurized, it’s dense, etc), and then use the nuclear powered electricity to generate your H2 and O2 and use it as fuel for your other ships.