I don't own a Mini-30, but I have tried to keep up with any issues others have had with theirs. Here's my take, from watching the forum:
You're right about the steel-cased ammo. It can cause jams for numerous reasons, and some have had firing pin issues, mostly with Berdan-primed imported ammo. This applies to the 18X, 19X series and the newer 58X series equally, so trading for a new rifle won't really be "trading up" as far as ammo and functionality are concerned.
Having said that, there are many here who have run steel-cased and Berdan-primed ammo for years without a single hiccup. There doesn't really seem to be a rhyme or reason for the firing pin breakages, as even some who have shot American-made commercial ammo (Boxer-primed) have had a firing pin break. Same goes for the Mini-14, as well. But don't think that the FP issues are rampant -- a handful of members here have reported broken pins, but they're quite vocal about their issues (rightfully so...), and it makes it seem like it's a large-scale problem. It's really not.
If you're looking for some cheap(ish) ammo for range time, the most-recommended brands are PMC Bronze, Fiocchi, Sellier & Bellot, PRVI Partizan, and Golden Bear. Basically, anything but WOLF.
As for hunting rounds, IMO you're best to stick with American-made, commercial ammo like Hornady, Winchester, etc. Brass-cased is best.
Again, I don't own a Mini-30, I've just "read the mail," so to speak. Others will be along shortly to weigh in with their personal opinions and experiences. YMMV.