I decided upon an octopus since the place where I live requires that any pet I have be able to live underwater. At first I had an idea for a small biosystem. I thought about getting some fish, some frogs, a turtle, and some other small creatures for a large aquarium. I figured that most of it would be water, with a shelf for some of the creatures who needed a place to sun and escape the water.
Then I read up on how the different animals would relate to each other. For the most part, the creatures would end up eating each other. Turtles seemed nice, but then I learned that they live anywhere from 70 to 100+ years. That was not something I was willing to sign up for. When it came down to it, I could have fish, snails, and some small frogs. It would be your basic freshwater aquarium. Determined, I went researching some more. What pets could I have? Then it came across me - my favorite aquatic creature, the octopus!
Note that I was willing to do a lot of stuff myself (DIY) and that cut down on my costs. In addition, I took my time, bought smoe stuff used and bought some stuff when they were on sale. If you are willing to do some of the work yourself and are willing to shop around, you can save some money. In the end, though, a tank for an octopus is still going to be expensive. Luckily my living arrangement is such that my employer pays for my electrical bills. This is a cost that you will have to factor in yourself.