Brick, i find either sleve anchors or resin is the best. If going down the resin route, you need to be carfeull not to drill right through, unless you are using the plastic sleeves aswell.
Decent concrete, thrubolts or thunderbolts.
Natural stone, and anything a bit soft, go with the resin.
If its only lightweight fixings required, nylon plugs and decent screws is aokay for just about anything.
Hilti do a fantastic chemical anchor and mesh sleeve jobby only use the Hilti chemical & the dispenser tool..
I have tried numerous other chemical fixing solutions but found that nothing came near the Hilti one.
The chemical anchors are not only absorbing glue into the brick work they are a stress free fix ...... So if you are going to hang the gate in a brick pillar you have less chance of splitting the brick work over time.
TIP
Start off with two undersize drills then carefully put in the final correct sized drill to give you a clean unbroken hole in the brick work.
You will need to be able to blow the dust out the hole .
They are temperature dependent for settting so if you use them read the info or you might come unstuck , leave them in place unloaded for the whole setting period plus a few hours.