Nostalrius Begins - Quality wow vanilla realm (1.12)

I plan to PvP and PvE, but I care more about PvP.

If you could choose one, would you go with Alchemy or Engineering?

I don't think Engineering is as godlike for Priests as it is for some other classes (Paladin), so I'm leaning more toward Alchemy.

Engineering will always be the best posible proffesion for pvp.

Net, Rockethelm (Priests have 0 mobility more like), MC cap, Rocket boost, grenades and reflectors.

Everything is useable and great for any class more or less.

So yes. Go with Engineering, you will not regret it.

Furthermore - You can get your pots and flasks crafted by guildies for free. I see no reason to be alchemist really.

Tailors get the best healing chest item until Nefarian (and even then it has more healing than the T2 chest).
Truefaith Vestments

As a second profession I'd prob take Engineering over Alchemy since pretty much everything an alchemist can make you can buy.