my favorite early and midgame setup is a mix of these, usually the former 4:
Burglar
Napalm
Iridium band
Slime charmer
Hot Java
Savage
Late game it's different, I am a player who thinks burglar is useless late game which causes a lot of arguments believe it or not, I have no clue in the world why people would think double monster drops are good late game but they can do whatevery they want. (If anyone thinks this or not, please list your reasons why, it's cool to see other peoples opinions and ideas).
Now I use:
Iridium Luck
Savage Luck
This combo is only really good in the mines and I have spent dozens of hours mastering the Savage ring which I think I can now finally say I am a pro at using (it is super hard to use to it's fullest, if you can it is one of if not the best ring in the game, especially for mining, in my opinion).
Otherwise it's ok but it's just over all nice, the luck is subtly nice in some cases and iridium is just overall good for most places.
I usully just rock this as I never need to change sets for any reason, maybe I might make an iridium band/immunity as a spare for the hard mode mines or the volcano but I haven't run them in ages, there is no reason too and while they are fun I have too much stuff ig and irl to do so.
Want to come in and change this a bit.
1. Slime charmer is next to useless, most of the benefit from it comes from negating the debuff, which leads into the second change:
2. Adding immunity band to the list, it's incredibly useful in places with heavy debuffs like the danger mines, pair it with mermaid or genie boots and you have effective immunity from getting any debuff, not just slimed
3. Hot java is one of those rings where you're almost always fine without it. It's not bad per se, but if there's a more useful ring then this should be first to go (unless you're using a really bad one)
4. Lucky ring is only really useful in the early game. While buff luck is widely useful, it's generally in such small degrees that it only meaningfully matters for a couple things, in which case they're better just swapped on temporarily (as outside of the mines, those things are incredibly niche and usually one time things, the casino and fishing for jellies is it basically).
Their prime use is obviously in mining, and even in that, they only really help with two things, treasure rooms (which is, similar to above examples, a pretty niche pursuit usually done on its own), and finding staircases. Having basically any amount of staircases being produced (even with just a few jade crystalariums), largely negates the benefit of luck however, and therefore it's usefullness as a primary ring massively falls off pretty much proportionally to the crystariums you have (didn't even mention previously that they're also getting you another permanent +1 luck in spicy eel), so it's not a very good mid/lategame ring.
5. Glowstone is really good as a combination with iridium band for 3 or 4x magnetism, which is actually fairly useful for large bombing areas