The dlc is good but not necessarily a prerequisite. Though a lot of content mods depend on assets from the dlc.

As others have said, the DLCs aren't strictly necessary, but it's good to have them. If you like playing modded, vanilla still has plenty of content. If you do decide to get a DLC I'd recommend Ideology, because it's the most meta-changing DLC.

I recommend playing the base game and getting back into the swing of things, then get the DLC that interests you most once you're hooked again. The DLC add a lot of content and can dramatically expand your play styles and experiences. There are tons of mods that can do the same for free too, and most don't require any of the dlc. My personal favourite DLC is biotech!

Note: I have played a heavily modded game with both Royalty and Ideology, not Biotech though.

None of the DLCs are strictly necessary, but I would highly recommend Ideology - the core mechanics it adds are compelling and impactful, and it serves as a nice base for a huge amount of mods to build off it. Royalty isn't bad either, but it seems more disconnected from the rest of the game than Ideology is.