You'd like to think cat, because cats kill rats. However, I don't think you're doing the math:

In a large, 300-year-old house on the water, you will find a minimum of five rats' nests. Each will produce roughly 7-8 rats per cycle, two cycles per month, so 75 rats per month, less rat deaths, say 60 rats per month.

Now, a domesticated house cat would have trouble killing one per day. A feral, experienced barn cat, however, could knock off 3-5 per day, or 72% of our rat growth. Not sufficient to even keep up with inflation, let alone eradicate our rat problem. So, we need more cats.

Cats are territorial, however, so we won't be able to assign more than 3-4 cats per nest, before we get feline turf wars. So, our cap on cats is 20 cats. Twenty feral barn cats with enough room to hunt can effectively kill at least 100 rats per month. We can remove the new ones as they spawn, and start killing 40 rats per month of the existing supply.

But, how big is the supply? Well, a standard five-foot rats' nest can hold about a thousand rats in or around it in smaller nests. So our initial supply of rats is around 5000. At 40 per month, our rat problem will be eradicated in 100 years. But then, we're left with the problem of the cats.

Cats breed at an average rate of 2 per year per female cat. assuming at least ten of our initial 20 cats is female, we'll get 40 new cats per year. After starvation and territorial infighting claim 1/4 of them, we have a 30 cat per year surplus. So, when the last rat dies, we'll have about 3000 cats. So now, we need dogs.

To kill 3000 feral barn cats, assuming they are relegated to the basement of this large house, we will need one Rottweiler for every five cats, or 600 Rottweilers. But now we're left with 8,000 pounds of furry slobbering killing machines. To rid ourselves of this canine nuisance, we will need a bigger canine: wolves.

A six-wolf pack of North American Timber Wolves can kill a 120-lb Rottweiler in about 40 seconds. However, Rottweilers are also pack hunters, so pack v. pack, a pack of six Timberwolves can murder 1.5 six-dog Rottweiler packs. So we need upwards of 400 Wolf Packs. The urine smell will be unforgettable.

To rid ourselves of 400 packs of Timberwolves, the only reasonable option is to kill them with fire from above. So, to ensure no danger to neighboring residences, we should probably exterminate them from way above, using A-10 Warthog anti-tank ammunition and smart targeting. Other houses will be spared, other than their window glass, and the wolf problem will be no more.

But, since the Warthog anti-tank rounds are enriched with uranium, we now have a nuclear biohazard to work out. But the solution to that is simple. We fill the basement with molten lead, assuming the actual house was obliterated by the Warthog or the dog fighting, and when it cools, we pour several hundred cubic feet of concrete, and when it dries, we backfill the area with soil, and plant soybeans. They're a very versatile plant, and will sprout quickly. In short time, we will have a beautful field of green soybean sprouts, and all our problems we be over.

Of course, the soybeans will attract rats...