1 Gate expand and 12 nexus (which can even defend double proxy rax) are common openers, and one can also go 2 gate chrono stalker.
Against Mech[]
It is important to scout for 4-6 factory attacks. One should go up to around 7-8 gateways and chrono out zealots while getting rushing for charge. The initial stalkers should wait for the terran in front of their army and kite as the terran moves across the map. Observer control and army movement in this situation is very important.
Try to avoid attacking a sieged position. Rather, try to use your mobility to force the Terran player to constantly having to reposition his army. If the Terran player tries to push, make sure to keep your army close to his, so he has to slowly move out, thus buying yourself time.
If you have to attack a sieged position, make sure you have at least one of the following: Observer to detect spider mines, Corsairs to lift tanks, High Templars (for storm), Zealots with speed, Warp Prism for drops, and most importantly, Arbiter for stasis
Against Bio[]
Unlike Brood War, Terrans do open with bio on some occations in Starbow. Stalkers with blink are excellent at kiting off Marines. Make sure to get the range upgrade at the Cybernetics Core. Transition into either Reavers or High Templars if the Terran player persists with the bio play. Watch out for Banshees and keep scouting for a mech transition.
There has also been some experimentation to use Scouts versus marines with some positive results. This, however, is not fully explored yet.
The Terran player will often try to expand more aggressively if they play bio than they would playing mech. Try to deny expansions as much as possible.