When fighting the Terrans as Protoss there are a few things you’re going to have to look out for no matter which strategy you plan on using. An aggressive Terran player will likely send either an early Reaper or an early Marauder to your base. This can be tricky since Reapers are good at killing Zealots and Marauders are good at killing Stalkers.
Since Marauders can be in your base earlier than Reapers, it’s a good idea to get a Zealot before you get your first Stalker. This way you’ll be protected if a Marauder gets to your base very early. There will be a small window where you could get a Reaper in your base, but you should be able to chase it around with your Zealot and a couple Probes until your Stalker gets out and you can finish off the Reaper.
As a Protoss player, your Probes are the most powerful worker units in the game. You should use them at the beginning of the game to harass the Terran SCVs. Since SCVs have to manually build their structures you can run up to the SCV building his first Barracks and attack move near it to attack it. You’ll be able to do some damage to it and it will force Terran to bring up another SCV or 2 to fight you off.
This will lower the Terran players income a little bit and is also extremely annoying. Fight the SCV’s until your shields are down, then retreat and let them recharge (it doesn’t take long). When your shields are back to full, go attack an SCV that is damaged and try to take it out. Keep doing this as long as you can and you’re sure to get into your opponent’s head.