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Humble folk of the cloth, Priests are not especially adept at combat. However, they tend to have a remarkably high constitution due to their vegan diets and morning aerobics sessions, which comes in handy when someone has to go deal with a local undead infestation. Stupid undead.
Halfling priests ( Halfling Priest) are generally the best race choice for Priests. The Halfling's ability to obtain mass amounts of Health Potions synergizes well with the Priest's increased maximum Health and 100% health potion effectiveness. This combination is able to produce the highest health spike from among all race-class combinations. Some items to consider: Alchemist Scroll and Trisword, both of which capitalize on the Halfling's more abundant health potions.
Orc priests ( Orc Priest) are a balanced combination. Combining the Orc's increased base damage with the Priest's increased maximum health makes them decent melee fighters. They are especially strong against undead, as the Orc's increased base damage synergizes well with the high bonus damage Priests have against undead, allowing for undead enemies to be taken out extremely early. Combined with first strike (a Getindare glyph, for example) an Orc Priest can eliminate very high level undead enemies.
Dwarf priests ( Dwarf Priest) can reach very large amounts of max health - actually, this combination has the highest amount of maximum health from amongst all race-class combinations. While they are generally inferior to Halflings in terms of their health spike, combined with other %-based health restoration abilities, like the Sanguine ability available via Dracul's boon, or the Fire Heart item, they can provide an interesting alternative. This combination is also the best to finish the Priest Gold challenge.
Any race apart from the halfling can expect to have up to 5 healing potions (one starting one, three found in any level and one from the shop). Halflings can be comfortable with using potions to level up, but other races are better served by conserving their health potions for the boss fight. A gnome or goblin priest can use their mana potions and dings respecively to help the priest level up using glyphs - which is more helpful than one would expect.
The Priest is a tanky sort of class, and his forte lies with his Health Potions. This makes them lean towards a more physical-oriented class, although they can work with glyphs too.
By far the best trademark of the Priest is the "Good Drink" trait, healing the Priest completely with a single Health Potion. This alone will let the Priest handle a great deal of tough enemies. If you can save enough health potions for the boss, the Priest can take care it easily.
Good Golly is a rather situational trait. It does effectively overcome the Zombie's high health, as well as reducing the effectiveness of the Wraith's physical resistance. It's even greater if you know the boss is an undead. Use this to your advantage to get those early level catapults. However, it should be noted that if you have found the sub dungeon containing Pepper the Dog and declared it a lockered item, you can "mark" a boss as undead, gaining an enormous advantage in the endgame.
As for Gods, Glowing Guardian is a big no, because he doesn't allow you to exploit your health potions without taking a serious hit to your piety. Jehora Jeheyu is a great god for the Priest to worship thanks to his Boost Health boon. An investment on a single health potion for 25 max health can go a a long way. The Earthmother is also not a bad choice, because her Vine Form boon is pretty cheap, and the Earthmother is a great source of piety. Combine this with The Pactmaker's Warrior's Pact for a large boost to your HP. Dracul could work, if you can get Sanguine up to significant levels. Combined with a decently leveled Sanguine and the Priest's naturally high health allows you to heal quite a large amount of health. You do get penalized for drink Health Potions, but it's not as bad as the Glowing Guardian. Alternating between Sanguine and Health Potions will ensure you won't get punished big time.
Obviously, items like the Tri-sword and Alchemist's Scroll work very well with the Priest, allowing you to get great leverage out of them, thanks to the Priest's natural dependency on Health Potions. Naga Cauldron makes potions overheal even when you are not debuffed, giving you 100% HP every time.