Aside from Utopia, which was already mentioned and is a must have, I like Megacorp, Overlord and especially Machine Age
Utopia. Hive minds and megastructures.
Utopia hands down, it was the first dlc for the game and added many features now considered core parts of it. Federations is also a must in my opinion, but that is more up to personal taste.
Aside from those two I would just read up on the packs and buy what sounds cool to me. At least that's how I did it back in the day when I started playing.
E: also note that paradox recently introduced a subscription model as well, which gives you full access to all dlc while you are subbed. This may be a great option to dip your toes and try out the content before buying it.
Thanks for the hint about the subscription! Given how many DLCs there are, this sounds really economical.
Yeah it is a great way to catch up as a new player, but it may also he a bit overwhelming, adding to the already steep learning curve.
Alternatively you can also join a multiplayer lobby with for example a friend who has the dlc, you can make full use of their features for the duration as well.
Also, if you end up deciding to permanently buy some, it is always wise to wait for a sale. All but the most recent dlc go on sale multiple times per year.
If you're coming in New I think the subscription is probably you're best bet.
Community for fans of the strategy game Stellaris.