Serpentis Armor Ishtar

Serpentis rats (which inhabit Gallente space in empire, and Fountain up to Fade in 0.0), do Thermal and Kinetic damage and have the lowest resists to thermal and kinetic damage, so there are a few ships that stick out as being excellent for combating them. Primary among them is the Tengu, but that can often be a bit pricey for some folks. You could try a Drake, but it ends up coming up short and is generally pretty low on DPS. The in-between option is the Ishtar. While it's more expensive than a Drake, and isn't as effective as a Tengu, it does have a number of advantages - namely, its versatility. Thanks to its massive drone bonus and innate resists in both shield and armor, to go along with a tiny signature radius, you can fit it any number of ways and still be spectacularly effective against Serpentis rats. Some people will prefer a passive shield Ishtar, or a dual-MAR Ishtar, but here's my preferred fitting:

[Ishtar, exploring]
Medium Armor Repairer II
Shadow Serpentis Armor Kinetic Hardener
Shadow Serpentis Armor Thermic Hardener
Shadow Serpentis Armor Thermic Hardener
Beta Reactor Control: Capacitor Power Relay I

Omnidirectional Tracking Link II
Omnidirectional Tracking Link II
10MN Afterburner II
Cap Recharger II
Cap Recharger II

Prototype Cloaking Device I
Heavy Electron Blaster II, Caldari Navy Antimatter Charge M
Heavy Electron Blaster II, Caldari Navy Antimatter Charge M
Heavy Electron Blaster II, Caldari Navy Antimatter Charge M
[empty high slot]

Medium Sentry Damage Augmentor I
Medium Sentry Damage Augmentor I

Garde II x5
Ogre II x5
Hobgoblin II x5

At all level V skills, this setup is cap-stable, tanks 476 Serpentis DPS, and avoids a healthy chunk of incoming damage thanks to a 145m signature radius and 614 m/s top speed. The Gardes do 538 DPS at 45648+12000, and the blasters add another 167 DPS at 1500+3800. Although it has 3 faction mods on it, they aren't too expensive, especially compared to the rising cost of t2 hulls.

Using the Ishtar is almost trivial. Turn on your mods, aggro the rats, deploy your drones, and orbit them at 5k. Kill the scramming/webbing frigates (or towers) first, then the destroyers, then the battlecruisers, then the battleships. Once you're down to only the long-range battleships, there's little enough incoming damage that you can stop orbiting and center yourself in your drones (the BSes orbit you at 51km, so if you're orbiting your drones they'll actually be around 56, which kills your damage). You can also fly around to pull the long-range BSes closer, but I'm too lazy to do so.

Practically speaking, it can solo almost anything you'll find. The exceptions I've run into so far are the Serpentis Prison Camp final room, the 2nd room in both stages of the Shadow Serpentis Fleet Staging Camp, and the final room of the Serpentis Provincial HQ first stage. [I'll keep this updated if I run into other things].

This Ishtar has the added bonus of working well if your skills aren't perfect. To start with, its damage isn't affected by your Heavy Assault Ship skill, only the drone bay - the drones I've listed above fit with only level 3. Additionally, if your cap/gunnery/fitting skills aren't perfect, you can pull the guns off, slap on a civilian gun, and replace one of the Cap Rechargers with a Cap Battery, which should put you comfortably cap stable without losing a ton of effectiveness. The guns aren't essential, they just let you shoot any frigates that get under your Gardes without having to scoop them and deploy Hobgoblins.

Another modification you can make, if you feel safe in the space you're exploring, is to pull the cloak off and upgrade the guns to neutrons, letting you largely ignore the frigate rats with your drones and save them for your guns where you can really mow them down.

The main advantage this fit has over the passive Ishtar is the afterburner. It makes a surprising difference in how much damage you have incoming, and also makes sites that have multiple gated rooms much more tolerable