Grinding the Honor Gear Which Honor pieces are best to get first?

Human Windwaker Monk with a Flying KickWhy the honor gear? Because it makes the RBGs and Areas, while earning your Conquest points, less painful. You can, if you want, skip the honor gear and go straight to grinding the conquest gear, it’ll just be a bit more painful at first. You might want to consider at least grinding for the honor weapons.

Which Honor pieces are best to get first?

If you don’t already have the PvP escape trinket you should get that first: Tyrannical Gladiator's Medallion of Tenacity
Which items really need upgrading (e.g., green questing items.) Take care of them. These will be your biggest gains.
For the rest of the gear, the Tyrannical Gladiator's Ironskin Gloves are a good first overall choice for the ability to break free from snares and they’re part of the set.
Otherwise, get the bigger pieces. They have better stats.
After earning the first 4k Honor save the rest. At 7,500 total earned you’ll have 3.500 and can buy your weapon(s.)
Also consider working for the 4 piece set for the PvP stats and their 4 piece set bonus, which is something of an “execute” ability. (see it here: Tyrannical Gladiator's Ironskin Tunic)  You need any four of: gloves, helm, legs, tunic, shoulders.