Limone Su Garda is not served by train so you will need to drive, bus or ferry there. You can ferry from Peschiera del Garda (2+ hours) which is a few minutes by train from Verona. Or from someplace like Malcesine which is much closer (20 minutes) but you will need to take a bus to or drive to Malcesine.
From Verona airport there's a short airport bus ride (15m) to Verona Porta Nuova to Peschiera del Garda, Italy (15m) and then walk to the ferry station and ferry to Limone Su Garda. There are bus options that get you closer but are not much faster than the ferry.
Milan MXP is an hour outside Milan and then Milan you can either train to Desenzano Garda-Sirm (1 hour) and the ferry to Limone Su Garda (2 hours) or to Brescia and take 2 buses to Limone Su Garda.
Venice is a bus or taxi to Venice Mestre and then 1 hour to Peschiera del Garda which may direct if you get lucky or change in Verona.
So Verona is closest but none of the transportation are easy or great. If you want to throw money at it you consider an driver to take you there but it will not be cheap. Or you could rent a car since the drive from the airport is about 1.5-2 hours.
If you search the forum there are people who have taken the train to Rovereto (1 hour) and then used a local driver to get around the lake. Those threads include a local driver recommendation. Rovereto to Limone Su Garda is probably an 45 minutes to an hour depending on traffic.
Hope that helps, have a great trip,
=Tod