There's actually two completely separate games (Java edition and Bedrock) that can't cross-play with each other. You can buy a Bedrock edition Minecraft for Windows that should be able to cross-play with the switch.

Java Edition is the original game and it's fairly easy to either host your own server (The dedicated server is just a .jar you run) or pay for a server ($10-40/mo) using a game server host.

Unsure about bedrock, there's some instructions here (https://www.reddit.com/r/Minecraft/wiki/bds/#wiki_bedrock_de...).