My son did the Suzuki method at an early age and it was fun. As a result, he was able to progress in his teens, after a long break from the instrument.
Also, even a cheap violin can sound ok. In fact, if a player is really good, close up I
struuggle to hear much difference between it and a more expensive one.
Nylon string cheap guitars seem to sound reasonable, but not so sure about cheap steel strings- and then there's the action to be considered.
If it's only adoring parents in the house, the agonised sounds are not such an issue, I suppose.
Another thought is that in the folk tradition, you would have a better chance to learn inexpensively.
To sum up my thoughts:
easier to go from violin to guitar than vice versa.