A fiddle and a violin are the same instrument but played in different styles. A piano background is very helpful for a violin player at the advanced levels because piano is a requirement for advanced music theory understanding (and test taking).
Here is our cautionary tale:
We stayed with a "wonderful" teacher that the owner of a music school referred us to (her employee). After 1.5 years with her, my son had progressed a lot, but was hitting a wall and could no longer progress. He was staying at the same level for months and struggling despite longer lessons and more practicing. I found a piano teacher referral from MTNA (music teachers association of north america) and asked her to evaluate my son. She pretty much said that many of his basic techniques were sloppy and he was playing well because he was compensating for his lack of technique with his intellect. She predicted that such kids end up dropping out of piano after a few years of lessons.
I was concerned about repetitive injuries from not being taught basic techniques correctly as well as taken aback that reputed music schools in my area did not have minimum standards for teaching or student evaluation. So, from then onwards, for all my son's music classes, I choose a teacher certified with a National Teacher's Association who also offers exams where my son can be evaluated by outside judges for his technical merit and his skills. I read all the comments from the judges and discuss them with the teacher. I make sure to ask if prospective teachers have a Master's degree in the instrument that they teach and if they have training in pedagogy for that instrument study (turns out that the person who originally taught my son did not have both of those qualifications). These have become very essential to me because I don't want to waste lesson time to find out later that some things have to be relearned.
Follow the teacher who are teaching the top instrument players in your area, request to attend their recitals, ask for a trial lesson before you take the plunge with any teacher.
A keyboard may not work well when your son gets to intermediate level piano and the teacher might even insist on an acoustic piano (they do, in my area). They will refer you to rentals if you want to wait to buy. Good luck.
