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I write elsewhere that I've got a mandolin, but the only thing I've ever done on it is strum along to Bob Dylan's Wagon Wheel.
Maybe I really should buy a pick and learn to play it Italian/Neapolitan Classical style. But I'm not sure how much I need to do to get there, apart from practise. Just buy some music and go for it, or is there some basic technique I need to know? Just play violin music on it? Is there a recommended book? Is there a Youtube channel? Are lessons necessary (please say no, as all my money is going on violin lessons already)? I guess all the technique will be in the picking. (or do you call it a plectrum?)
You can use the same sheet music. With practice you'll learn the idiosyncrasies and character differences. There are quite a few YouTube videos, some from bluegrass greats. There are also videos of guitar players playing the mandolin like a guitar.
Starting off, master alternate picking(up-down-up-down) as it gives you the most speed. There's cross picking but that's not something a beginner needs.
Get a collection of picks together of varying thicknesses and materials. They're cheap so might as well get a variety.
Tremolo is a skill that will be most important skill needed in that style. Tremolo is rapid picking of a note in succession. You may find one pick type may work better for it than others. In bluegrass styles you'll want to eschew open chords and learn to chop them rhytmically.
If you can already read sheet, you're already ahead. Though mandolin is mostly a folk instrument, vivaldi has composed music for it.
If you're mostly focused on violin, the mandolin can make a good secondary instrument to it and I don't see the need to get formal with it unless your heart is set on it(for example, Sam Bush was a fiddler but he's most known for his mandolin playing).
For me, the mandolin is just there when I'm in the mood to pick because sometimes you're just in a picking mood. It's not my main instrument.
Thanks @Amateur I'll look for some of that Vivaldi in IMSLP.
Our uke group does Va Pensiero (Verdi) often with our leader picking mando. He's in his 70s now and weighs as much as you and me put together, so I may need to take over from him. Otoh, he can carry his 4 or 5 instruments in his 4x4, whereas I'm not even going to try on the bus, lol!