u/ConsistentCut7788

For context, I’ve played string instruments like the guitar and ukulele for several years. Now, I’m torn between choosing the violin or the saxophone(alto). I'm considering the sax because I want to learn a wind instrument, and I love the jazz music played in restaurants. One thing holding me back is the introductory price(around 20k) and the learning curve.

Is it that difficult to learn? Do I need formal lessons?