Profession for a PvP PriestFollow

Is it your only character?

There's a primary consideration regarding engineering: only engineers can use most of the items. Thus if you want stat-boosting goggles, bombs, dynamite (for AoE attacks) etc you will need to make engineering one of your choices. For other professions, an alt or a guild-mate can make the potions, armor etc that you need and mail it to you.

Enchanting is the other thing an alt can't do for you (can't send soulbound items back and forth) so that would be the other choice for self-sufficiency if you don't want to rely on guild/alt supply.