Parents of a school children should vote with their money.
It wouldn't work. I have a supervisory position in a private school, and if parents were allowed to vote on individual teachers, you'd see a lot of problems with teachers doing things such as giving easy work (so the kids get high grades, so parents are happy) instead of doing the right thing. It's a problem where I work - one of the most popular teachers is also a crap teacher, but because his subject is never tested externally, no-one cares because the parents and kids love him. However, he sucks and he doesn't have a clue.
There are ways to evaluate teachers, and parent/child evaluations are part of the overall puzzle, but you should also be evaluating (and paying) them on objective criteria. But to go back to your idea about skills and results - skills, yes. Results are trickier, because it's not fair to punish teachers financially for having weak classes. If it was up to me, I'd broadly pay teachers according to their qualifications, experience, subject knowledge (and yes, it should be tested yearly), evaluations from management/parents/children, extra activities and their actual work (are they organised, are they effective, do they follow the programa podstawowa correctly, etc.).
So yes, great teachers who have high qualifications, lots of experience, great subject knowledge, good evaluations and who put a lot of effort into what they do - they should be paid well. Those who do the bare minimum deserve the bare minimum, IMO.