What do you usually upgrade first - cartridge or phono stage ?

What, only one or the other? Not a few of each at once? That’s way too little chaos for me to enjoy a hobby with...

If you have one egregiously below level of the other, then do that one. Otherwise, get which you fancy more; it doesn’t really matter. New cartridges are probably a better dopamine hit (on average) but phono stages can stick around for multiple carts, don’t need alignment, and don’t wear out (so much). 

A few of each at once, right.

New phono stage can bring out everything your old cartridge is capable of, and new cartridge will likely sound better than the old one with the old phono stage.

The world's best cartridge will not sound great with the world's worst phono stage but budget cartridges will benefit from the world's best phono stage. Best to buy the best performing phono stage you can afford and work your way up to a cartridge which equals the the phono stage.

Before cartridge and phono stage get the best turntable and arm you can afford. Buy second hand if prices are intimidating,

That's generally my thinking as well.

Get everything possible out of your excellent cartridge and only then upgrade it.

Similar with speakers.

I had a Goldring E3 mounted on a Rega P2 and was using a very decent phono stage built in with Rogue RP1.  Sounded great. Then I tried the Mcintosh MP100 phono stage I borrowed from my buddy and my jaw dropped. I paid $100 for that Goldring. It sounded insanely good. I had to return the MP100 and continued using the built in phono. Later on I stepped up to Hana EH cartridge and while the upgrade was very audible, it was nowhere near the level of improvement brought by the upgraded phono stage.