Depends on the species and what you are mixing together I suppose. Adding something territorial like cichlids requires some planning in advance for example, whereas it may not matter with more peaceful community fish.
Usually any fish I already have in house that was slated for the new setup goes first. Following fish have to do a Q tank stint before moving on up to the east side. I favor friendly fish so aggressive / territorial issues are not usually a big concern.
The first fish I add are hardy or beginner friendly fish. Such as Platies, Cherry Barbs, White Cloud Mountain Minnows, Zebra Danios, etc. As you research care sheets and other info sources will mention if your specific fish species is hardy or beginner friendly. If the fish need groups of their own kind I'll usually add 3 fish or so at a time, wait a few days, and then add 3 more etc. until I get to the full school number. If you add too many fish at once it can cause spikes in Ammonia.
I like to add in algae eaters and filter feeders somewhat later on, so that the tank has already been setup for long enough to establish algae and micro-organisms. Things like Otocinclus Catfish, Bristlenose Plecos, or Bamboo Shrimp do better with a tank that's been established and ideally has had live plants for a few months.
Then there's territorial fish, like many Cichlids, that will often accept tank mates more readily if the other tankmates are already in the tank before the more aggressive fish is added. If for some reason I have to add an additional aggressive fish later on, I'll at least rearrange all the decor to break up existing territory lines and give everyone an equal chance at establishing territories at the same time as I add in the new aggressive fish.
Fragile fish that are sensitive to water quality I only add after the tank has been established for 6 months or more. Neon Tetras, Glass Catfish, or Red Crystal Shrimp for example. Established tanks are less likely to have traces of Ammonia or Nitrite. Again, if you research the fish thoroughly you should come across care sheets mentioning if a fish does best in established tanks.