I am an avid user and supporter of ring swapping though do it less now because of 1.5 and being in a late game farm.
Keep in mind this is the perspective of a player who loves the SC and excels at combat and slingshot as well as having near infinite money for bombs and eplosive ammo (which is so broken, even in 1.5).
The rings I use on pc in the mines and for causal wear are iridium band with luck and savage with luck. Some people opt for double iridium but I never do so unless in mid game without a better ring to combine. I agree with
Cptldsilver on his point about the savage being really bad if you don't know how to use it but if you are an experienced player in a later-game farm it is a great ring to combine with.
The luck rings are also just way too good to pass up on, wearing them both and having optimal buffs (magic rock candy, gold star ginger ale) can net you a +9 luck buff which is mad and even with only a +6 buff (rings + gold lucky lunch), I found 10 prismatic shards and got to floor 183 without staricases.
I always carry two combined rings around anyway for nostalgia and for niche purposes, they are a napalm/slime charmer and hot java/burgler, they both go pretty heavily underused but used to be my main rings and are my go to for early-mid game.
I used to play a lot more mobile and have a good hilltop farm which I cavern dive quite often too, I have four rings and they are the burlger ring/napalm/iridium band/slime charmer. The first two I use for mining and the others just casual playing.
That's pretty much all I have to say without going out on a tangent about the rest of SC.
Good luck.