What is the best way to get from Linate to the train station in downtown Milan??
By bus there is the Linate Shuttle.
https://www.milano-aeroporti.it/linate-shuttle/index.html
The train station in downtown Milan would be Milano Centrale or Milano Cadorna? Or Milano Garibaldi?
Most buses and shuttles go to Milano Centrale, but the answer to your question depends on where you are actually staying. You could even take the new metro from Linate airport to Milano Dateo station and take a train to somewhere else