LaVaux Vineyard from Montreux?

Where should we go by train from Montreux to visit LaVaux Vineyard? We are mosts interested in a pleasant walk (more so than a hike) in the Vineyard and doing a wine tasting at their tasting room. We are not looking for a 'wine train' through the vineyard as much a seeing the place and enjoying some wine and snacks at their tastiing room. Which train station should we go to for getting closest that those things? Lutry? Vevey? Other?

Thanks much!