No, you definately wouldn't want that 3pak as you don't need carbon, and definately not ammonia remover, in your filter on a regular basis. What you generally want in a larger external cannister like you have is a couple of beds of ceramics, with possibly coarse and fine sponges to top them off and then maybe a final layer of floss or equivalent fine filter pad to catch the smallest particles.
In larger filters where the there is enough room for a layer of "ceramic rings," or "noodles" as they are sometimes called, to be 3 or so rings deep or more, they can do a good job at serving a couple of functions: they "randomize" the directionality of water flow. This slows the flow and ensures that the water moves in different directions so that it encounters more media surface area and can't take "short cuts." Meanwhile the surface of each ceramic ring itself is very porous and designed to be an optimal growth medium for autotrophic bacteria. The weight of each ring also helps it redirect water rather than being simple rattled around by the water. This layer of ceramic rings can be capped by a coarse sponge, which serves as a tighter catch for larger particles while still being an excellent biosurface for still more beneficial bacteria.
Next in the water path might come ceramic gravel, having the same optimal type of rough ceramic surface as the rings, but packing itself into a layer that forces the water through significantly smaller spaces, thus serving as a mechanical filter that can catch smaller particles than the rings and coarse sponge. This layer might be capped by a fine sponge to help again with both mechanical and biological functions.
Then finally the last media in the water path is the optional fine filter pad or layer of polyfloss or "floss" as its called for short. This sort of layer can become clogged more quickly and usually will break down sooner but can be periodically replaced as it does not become the critical storehouse of beneficial bacteria like the other layers do.
Carbon (aka charcoal or activated carbon) is a great media to have on the shelf ahead of need but is not beneficial in the normal month to month running of a filter. It is used to remove medications after they have finished their course and to remove yellow tannins that might still be leaching from decorative wood you have put in your tank that has not fully aged yet. Carbon is also good for removing organic smells if they should crop up as an unexpected problem. Zeolite or other "ammonia remover" materials are even more specialized than carbon and are sometimes used in difficult emergency situations or by very experienced aquarists running more specialized tanks. It is not a good media for beginners usually. Both Carbon and Zeolite are examples of "chemical media," the optional third function of filters after the mechanical and biological functions. All media overlap these different functions to some extent but each type is generally optimal for one particular function.
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