There are several shops that do mini-14 trigger jobs for about $70. I have not worked with any of these shops, but Brimstone has a good reputation. Google will find you more options and reviews.
One of the nice things about the mini is that you can just send the trigger group for a trigger job, so you don't have to pay to ship a firearm. You do need the insure the trigger group though, because a replacement trigger group costs about $350 if you can find one.
If I wanted a better trigger on a mini, I would let one of the professional shops do it. When people talk about polishing triggers, they are usually talking about a double action revolver trigger. The double action triggers can often be improved with polishing.
Single action is a different story. The surfaces for single action triggers are much smaller and more precise, and single action triggers require much more knowledge and care to work on them. Often specialized jigs and stones are necessary to make improvements without compromising safety.
The two stage trigger on a mini-14 is pretty much a single action type of trigger. And Ruger tightly controls the parts for the trigger group, so it is difficult and expensive to get replacement parts if too much metal is removed. If you are not already familiar with working on these types of triggers, I would suggest that the mini might not be a good first project.
Good luck with whatever course you choose. The stock trigger in a mini is pretty tough, and I'll be interested in a range report after you get a trigger that you like.