I'm in the same camp as
@boltfluter . Don't over clean. That said, I rarely buy a new rifle scope, I much prefer the cost advantage of purchasing used. My hope is the previous owner never cleaned the lens, but took reasonable good care of them. And usually that is the case.
But that said, most I purchase are in need of cleaning. I spent a lot of time reading advice on lens cleaning. Mostly on photography cleaning since there are more articles. And there are specific steps to follow.
1. remove any loose particles on the surface. I found the typical blow-brushes inadequate since they lack volume you need to accomplish this. The bulb type "hurricane blower" offers much improved effectiveness at this. When I am hunting in dusty condition like most days on a prairie dog hunt, I use the blower every night when I finish. Don't wait for days to let it accumulate.

2. a lens brush should be the next step. Don't scrimp on this, you want a quality brush. And if you ever use it on a lens that has had some oil residue present on it, throw it away. It will be contaminated, and spread that on any lens you clean in the future. And this is fairly common on rifle scopes. Folks use spray bore cleaners without using lens covers in place. And after lubing your bolt, the first few shots can atomize the oil into small droplets and can wind up on the lens.
3. When I have material on the lens that must be removed, and steps 1 & 2 haven't done the job. I use ROR (Residual Oil Remover). I've tried all the other recommended liquids and some of my own, and they all leave a residue as they finish drying. ROR is excellent for removing oil, and other materials from the surface of the lens without attacking the coating. I buy the spray bottle dispenser (also available in a dropper bottle) and very lightly mist a virgin cotton ball. I clean the lens with that, and use several virgin cotton balls to keep wiping the lens until it is dry. DO NOT drop liquid or spray liquid on the lens directly! This has always removed any foreign material on the lens and never leaves any residue. But once I clean a lens this way, I keep it protected so I avoid the future need to do so. The oil on your skin can contaminate the cotton ball, so be careful about how you grip it, where you set it down when you are using them.
And ALWAYS avoid breathing on to the lens to moisten it for cleaning. You will expel liquid and other particles you don't want on your lens. And of course never use your shirt tail to wipe a lens.
There are many methods to clean lens, some listed above, so you just have to decide what method works best for you. This is what I have found works best for me.