You'll want to use the official site of Trenitalia which is the state train company of Italy: https://www.trenitalia.com/en.html
They also have an app for use in country that also let's you track trains in realtime and validate tickets etc. Use the Italian city names for best results when searching on train sites: Roma for Rome, Firenze for Florence and get used to 24 hour times for train use.
Local train tickets - called regionale - do not come with seat reservations, never sell out and always the same price so buy them when you need them. Tickets in the app need to be purchased a minimum of 5 minutes before the departure time and validated in the app a maximum of 1 minute before the departure time. Paper tickets are available from train machines and these should be validated in the stamping machines as you approach the tracks.
Google maps transit tab does a good job with local city buses but longer distance companies tend to run independent of one another especially when you move from region to region. Buy local bus tickets at the T sign labelled tabac shops although this is less dependable in Verona since you can buy tickets on board buses at a slight up charge. I believe it is 2e versus 1.4e a ticket pre-purchased. The bus system in Verona is consolidated outside the train station so local, airport, longer distance buses mostly leave from there.
The bus company that runs the buses from Verona to Simone directly is Arriva and they have an app: https://brescia.arriva.it/en/
The company that runs buses along the east side of the lake from Verona is call ATV https://www.atv.verona.it/en/LineeLago
The places like Omio and Moovit are consolidated third party sellers for buses. They can be helpful for schedule, line or map information but I would always prefer to buy from the carrier directly if possible.
Similarly there are many taxi apps but I've had good luck with AppTaxi in the Veneto area. There is, of course, a taxi stand outside the train station and one deep downtown in Piazza delle Erbe.
Have a great trip, the transit system in Italy can be intimidating at first but it is the way the locals get around and is easy once you get used to it.
=Tod