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May I suggest that you try using the Cities Skylines Wiki pages ("Skylines Wiki") for very helpful information, hints and "pointers."
Regarding your direct question on garbage, please visit this page, and especially scroll down and read the "Strategy" section .... http://www.skylineswiki.com/Garbage_disposal
Use the "Search" box (near the top-right corner of the page), and enter other Cities Skylines topics that you may have an interest in.
Hope this info helps you.
To be more direct. Incinerators are all you need. Landfills are just there to provide an incentive for you to grow relatively quickly to get to incinerators before your giant mounds of refuse choke the life out of your city.
Funny. I was thinking the same thing just a few minutes ago.
As it turns out, from the Wiki, incinerators is the way to go. Which sucks as they cause a lot of pollution. Why doesn't CS have a 'vanilla' recycle centre available? I could use one of the many mods but, it doesn't feel right.