55 gallon sounds like an okay place to start, depending on the size of the animal you end up with.
Recently
@Bill Walton started a thread about his octopus keeping experience. He did a great job sharing relevant information about his setup, which looks good to me. You can read about it in
this thread here. It should be a good starting place for you to learn and think about what kinds of parts you will want for your system. You will want a protein skimmer in addition to the filtration that the tank comes with. If the tank only has inbuilt infiltration (the entire setup is just one box) it likely will not work to house an octopus. You will want two boxes, a tank for your animal, and a sump (a secondary tank with all your filtration and pumps and heater and stuff) that rests underneath the tank on the floor.
Bill started his system with some saltwater fish, which I suggest you do as well. Octopus are quite expensive (sometimes upwards of $150) so it would be a shame to buy one and put it in a system that wasn't properly cycled yet.
In terms of learning about the ammonia cycle and water chemistry, googling "saltwater aquarium ammonia cycle" turns up a boatload of great links and articles with relevant information. Essentially, before you will be able to have any animals in your tank, you will need to grow beneficial bacteria in the tank that will help to break down the waste produced by the animals that will eventually be in your tank. This generally takes about 3-6 weeks to do properly, depending on the size of your aquarium.
I encourage you to do some more research about water chemistry and ammonia cycles, as well as the filtration needs of octopuses. There were some forum threads in the links I shared with you earlier that detail this information, and there are plenty of websites that have beginner guides to setting up aquaria of various types. You will want to learn about chemical filtration, protein skimmers, pumps and water pressure, heaters, acceptable temperature and pH range.
In terms of shops that sell animals, you will probably have little luck finding them in stores. You will probably have to order some from a vendor. Once you have a tank set up and running then I can give more specific advice about sourcing an octopus, but your search may take a few months (perfect time to have some saltwater fish in your aquarium)!