Some observations on my first experiences with the new economy:
1. As others said, do not rush to fill the building slots of planets, that is a sure way to tank your economy - only build new building as you have pops enough to man them without taking workers from resource districts. A good way to know when you should build something is when the first unemployed pop shows up.
2. The most important districts are farming and mining, only build city districts as you need to keep amenities and housing positive and generator districts should only be built if you are negative in the energy generation or does not have anything better to build. Mid-late game, as your trade value increases, you should replace most of your generator districts to more useful farming and mining ones.
3. Agrarian Idyll (spelling?) is very strong now, if you pick it build farming districts until the max the planet allows and only them start building other districts - with agrarian Idyll you do not need city districts anymore for amenities or housing.
4. Be careful when upgrading some buildings, beyond the basic version research, alloys and consumer goods buildings start needing special resources, if you do not have a good supply of these resources you will start needing to buy from the market and the market prices are not worth it - normally you would have more than enough building slots unfilled until late game, so prefer to build 2 of the basic version of the building you need instead of upgrading a single building to the next tier - you should only consider upgrading research, alloy and consumer goods buildings when you start running out of building space on planets - and that will take a long time to happen. The only bulding that is worth it to upgrade asap is the gene clinics, as the increased growth rate is worth buying the needed resources from the market.
5. The best traditions now are prosperity and expansion (in that order) - diplomacy is good for the market discount perk as it will make easier for you to use the market to fill any deficiencies, specially in special resources.
6. Be careful before colonizing low-habitability planets, the increased costs can tank you economy. Migration controls are a must now to stop pop-types moving to low-habitability planets for their species - individual traits from the pops are a minor concern now , but pops moving to low-hab planets for their species can quickly kill your economy because of the increased costs.
7. Trade is very strong now, and by mid-late game should be your main source of energy. You should build two types of starbases to maximize trade: first a trade hub base with trade modules to collect the trade from nearby systems and second a pirate hunting base with defensive modules to patrol the trade routes to you capital as patrolling ships are too inefficient past the early-game. As you increase the stations sizes you will be needing less trade hubs and should be able to dedicate stations for other purposes, but remember that the patrol bonuses from pirate hunting stations stack with each other, so you may want to keep more defensive stations for the stacking effect.
8. Pop growth is the most important "resource" now, you should always maximize it in all your planets - always keep the planetary decision that increases pop growth up, enact and keep the pop growth edict (Healthcare?), and build Gene Clinics asap on all planets (Normally it is my second building built, after the robot factories).
9. Robots are good to quickly get more pops to work districts faster - all your planets should have robot factories built in them (it is the first building i create on new planets), even if they do not have districts for the robots to work on as you can resettle the produced robots to more useful planets. The most important trait now for robots is the one that decreases their production time (Mass-Produced) as it will increase the number of yuor robots.
10. Unity is easier to produce now and you should not rush to unity producing buldings, give preference to growth buildings first (robot factories and gene clinics) and only after you should think about building unity buildings - depending in your situation your research, alloy and consumer goods buildings are better investments - I like to alternate between a research/production building and a unity one.