I think that it is pretty hard to generalize. I like Savarez right now on my Mainland Mahogany tenor and my wife's Mainland concert sounds great with Aquila Nylguts. Try a Savarez set on your soprano.
I have Martin M600s on both of my sopranos. (One is a Kamaka pineapple and the other is a Kala KA-S--very different ukes!) I like them a lot on both; the Martin strings give both ukes a lot of volume and good sustain with a classic punchy sound.
The Kamaka is still new, and I plan on trying lots of different strings on it. Next up will probably be Worth BMs, then I will probably try Living Waters, which is what I have on my concert.
You need to provide more information so your question is not so open ended. Since you are "going around in circles trying to figure out what works best" I assume you have tried a number of brands and are dissatisfied. Which brands have you tried and why are you dissatisfied? And are you requesting information for a mahogany, mango, spruce, or cedar Mainland soprano ukulele? You've only received two responses to your question in almost a day's time. To me that indicates your question needs to be rethought.
A great document begins with the works, that we hold these truths to bw self evident. This ain't goona be a great document, but the same hought comes to mind. No one else has your fingers. No one else can tell how you like the way they feel. No one else has your eyes. No one else can tell how you like the way they look. No one else has your ears. No one else can tell how you like the sound. It's a lonely road that no one else can walk for you. Would you consider a minor tweak to the uke which might have a major change in the sound? It is, quick, simple and easy to do. If you want to know more, please let me know.
Generally speaking for the strings of the same material, the bigger the diameter the punchier the sound. If you attack the uke hard you will get better volume with larger diameter strings. If you are just learning the uke lighter gage strings are easier to play but heavier gage strings improve your muscle memory and intonation faster.
I think I had some old Aquilas on it that were good, but went flat and I went to replace with some GHS, which didn't work at all, and now it's got Koaloha Golds, inexpensive nylon, which don't do much either.
I've got a pack of worths in the box.
I guess the thing I'm looking for is volume here, and nice belltones. I'm getting a bit spoiled with the sound of the Kala LaSalle.
I am suprised more people have not recommended Martin M600. There seems to be a soprano string choice thread every so often and the M600 are always highly recommended. I use them on both my sopranos and they give great volume and clarity.
I like "TheCraftedCow's" answer........basically it is all very personal and only experimenting with different strings will let YOU hear and feel the difference. You have some good recommendations to go on now.
So many people rave about Aquila Nyglut or now I think it's Super Nyglut (which I believe are also the maker of the D'adarrio - however you spell it) but I'm not a huge fan. That being said, I very much think they are the BEST for a soprano given their brightness, feel, ability to stay in tune, and availability.
Your Mainland will probably come with them so I understand the desire to try something new, but I think they are best for that size.