I just recently bought the game + DLCs, and now I'm wondering about the best order to play:
- Install everything and just play or
- Play through the base game first and then DLCs after in order of their released date

Each of the DLC either add a class or a new dungeon/event and some mechanics. It is up to you if you want to jump in all at once or add them part by part. I believe you can add them to ongoing games.

I only played base game ages ago, but recently grabbed all the DLC and activated it all at once.

Two of the DLCs add not just extra "levels", but also extra... "stuff"... to the base game (which can help/annoy you when playing through the "normal" part of the game). It can be intense, annoying or useful... IMO I think it's cool to activate everything at once, but it can be a tad overwhelming until you realise you can (mostly) ignore the extra stuff till you're ready...

The other DLCs just add characters I believe (maybe one or two related events)? I'd activate all those "basic" ones without a second thought, as it gives you more (potential) classes to choose from.