Don't Starve Together server: why you are really running two
Don't Starve Together has a quirk you will not meet elsewhere: one server actually runs two worlds at once. The surface and the caves are separate processes running side by side, together forming a single game world.
Two shards, one server
As soon as a player goes down a hole, they are handed over to the caves shard. In practice that means your server runs two instances, both wanting memory and processing power. Account for that when choosing a plan — a DST server with caves is close to twice as heavy as one without.
You can disable caves if you do not use them. That halves the load immediately.
Worlds persist
A DST world lasts a long time and changes with the seasons. Because everything persists — bases, farms, cleared areas — the saved world file grows gradually. That is not a problem, but it is worth having backups before you start a new season.
Mods
Mods come from the Steam Workshop and are configured server side. Players are offered them automatically on connecting, which makes DST far more approachable than games where everyone installs manually.
How much RAM
2 GB covers a group of friends with surface and caves. For a larger public server with many mods, 4 GB is more comfortable.