Don't be discouraged! There's really nothing different about setting up a bigger tank other than the fact that the tank is bigger (and heavier). For starters, make sure you have a good stand that was built for the tank and be sure you're setting it up completely level on a floor that can support the weight of the tank. A standard 60 gallon tank weighs 710 pounds when full.
Essentially, you have the same things to consider when setting up a big tank. You need substrate (gravel or sand in most cases), heaters (once you get to that size tank you might want two heaters for even heat distribution) and filters. There's really nothing special about filtration on a bigger tank like that - you just need to be sure you're providing enough of it. On big tanks, canister filters are helpful because they can process a lot of water and can hold a lot of filter media (like filter floss, sponges, bioballs, ceramic rings, carbon, etc) however they certainly aren't required. You could get the job done with power filters just like you have on your 13 gallon tank, you'd just need bigger ones. Filtration also depends on what you're putting in the tank. If you plan on having lots of live plants, then you probably want to avoid power filters because they tend to cause a lot of surface turbulence, which releases CO2 from the water that your plants need. If you're getting big, messy fish (like cichlids) then you'll want to add extra filtration. For example, I have a 29 gallon tank that I'm going to put a Jack Dempsey cichlid in. Since these fish produce a lot of waste and are messy eaters, I'm using a power filter rated for a 55 gallon tank and a canister filter also rated for roughly 55 gallons.
When you choose the substrate, it changes some of your options. If you use sand instead of gravel, you can't use an undergravel filter. You also need to take extra precautions to keep your sand stirred up, either by doing it yourself or getting some sort of burrowing animal (fish like loaches or Malaysian Trumpet Snails) to stir it for you. Having sand has the benefit of letting you get fish that like the burrow or root through soft sand, plus it looks great.
Also, the lights you use on the tank will determine what kind live plants you can have. If you aren't interested in live plants, any sort of fluorescent lighting will work, but you'll need more expensive light fixtures for plants that require high lighting.
With a bigger tank like that, you have a lot more options when it comes to choosing fish to go in the tank. You could have big schools of small fish, or keep some bigger fish like mid-sized cichlids.
I suggest you figure out exactly what kind of fish you want to keep, then get the equipment you need in order to keep them. Then, it's just a matter of setting up the tank, letting it cycle properly, and then adding your fish.