The simplest way to beat Naga City is with an Orc Rogue with Glowing Guardian prepped. This is a strong enough combo that you don't have to engage in any god-swapping antics to win. Here is a simple set up that will win consistently and is easy to work with
Locker: Dwarven Gauntlets
Thief: Black Market
Church: Glowing Guardian (essential)
Mage Tower: Attack Boost
Blacksmith: Perseverance Badge
Bazaar: Extra Shop (convert for extra GG piety)
Potions: Burn Salve, Reflex, Quicksilver, Strength, Shadenfreude (sub in Whupaz for Burn Salve if you have it and lack confidence)
Alchemist: Compression Scroll
This is not the optimal set up, it is an easy set up. You can screw up or have bad luck and you will still be okay. The plan is to be a monotheistic follower of Glowing Guardian. Convert Health and Mana potions on sight. A better strategy would be to save your potions for a deity switch, but that is easy to screw up and we are trying to keep it simple here.
Immediately worship GG. Convert your Shop Scroll and take as many hits of Absolution as you can. As you explore, you'll want to convert any potions or glyphs you find right away,with a few exceptions. If you find LEMISEE, use it until you have located both stairs and the fireball glyph, and then convert it. If you find either ENDISWAL or PISORf, leave it on the ground until you know where the secret dungeon is. Convert it after you access the secret room. Keep the Fireball glyph. HALPMEH is probably even better, but we are going for simplicity here. Be careful buying things. You want to buy either the Midas Gloves or the Troll Heart. Save your gold until you know what your options are.
Use Strength + Quicksilver to get your first kill. You want to bag a or 4 or even a 5, but it's fine to settle for a 3. Throw in the Reflex potion if you have to. You're going to want to free up space anyway. Grab Humility right after leveling up and then keep Absolving as you can. You want your inventory to consist of your compressed Dwarven Gauntlets, your remaining potions, the Fireball glyph, one other item, and then the rest should be Prayer Beads. As you use your potions, replace those slots with more Beads.
You should be able to curb stomp the dungeon. Take Enlightenment at the first opportunity and then just kill everything. Usually you will want to tailor your experience so that you are just a hair short of a new ding before descending, but don't bother. Your Enlightened Orc Rogue will be a beast and doesn't need to care about such things.
Before you go down, convert your Troll Heart and/or Midas Gloves and then use your remaining cash to buy and convert what you can. Make sure that you leave one full slot open, because you will want to buy things down below.
With even passingly good technique, you should be able to demolish the arena. You'll have upwards of 150 health, 100 damage, and 18 mana. Use the gold drops from the bosses to unlock GG's altar, buy and convert the kegs, and buy the Yendor amulet, and roughly in that order. Remember that Cleansing converts your damage to magic, which lets you demolish the Tower of Goo and Tormented One.