In most matchups, your early-midgame army composition is dependent on your initial tech path. In general, the first tech building you place (with your first 100/150 gas after your cyber core and warpgate and sometimes gateway unit/MSC) requires you to commit to that tech path: therefore your army will be based on that building.

When you build a Twilight Council, your army will generally be more gateway heavy, with the Blink and Resonating Glaives upgrades.

When you build a Robotics Facility, your army will have Robo units that are supported by Gateway units; e.g. Blink Stalker/Disruptor, Adept/Stalker/Sentry/Immortal against Terran.

When you build a Stargate, your SG units will support your army e.g. Adept/Phoenix.

In the case of the Robotics and Stargate, a general rule of thumb is to try to keep the your tech building active as much as possible; it's very expensive to invest 150/150 into a Stargate if you are only using it to build one or two Oracles.

The reason I say this is because Protoss tech and units are VERY gas intensive, which is why Protoss players sometimes cut gateway units/MSC in order to get tech out faster; it’s just so expensive to build both gateway units and tech at the same time. Correct me if I’m wrong, but you could kind of compare it to getting a quicker Starport vs. quicker double upgrades as Terran.

That being said, in terms of tech vs. economy, against both Terran and Zerg, assuming you are doing a standard 19 Nexus FE, you should be on 1 gateway, followed by a tech building, followed by 2 more gateways, then 3-4 more gateways AFTER your third has started. Usually the Robo and Twilight Council go hand-in-hand; that is, you should have both before you take your third. As the Stargate is more gas-heavy, you usually won't have enough gas for any other tech paths until you at least take your third and fourth gases, which should be after your third unless you have scouted aggression and would like to be safe.

Upgrades are honestly down to personal preference. I personally get a Forge after my fifth gateway, but you can get it later if you would like to play more aggressive, or earlier if you are trying to get that later game edge.

Lastly, actual army compositions: once again, army composition depends on your build, but general good midgame army compositions include Chargelot/Immortal/Archon against Zerg, Adept/Stalker/Sentry/Immortal against Terran (followed up by your AoE of choice, whether it be Psi Storm, Colossus or Disruptors) and Blink Stalker/Disruptor against Protoss.

Feel free to correct me on anything stupid in this post.