College student looking to get into homebrewing, what is the essential equipment I need to get started?

I'm looking for stuff that is inexpensive, robust, and will continue to find a use as my brewing expands. From what I gather (reading what's in starter kits online) I need a fermenter with an airlock, a big pot (I have one that could boil about 2 gallons) and: cleanser, hydrometer, thermometer, way to clean my fermenter,way to fill the bottles,wort chiller?,yeast beaker?

Am I missing anything? How much of that stuff is essential to the process? Can all you experienced folk recommend me some equipment?

I'm planning on drinking a lot of these so I don't need to buy bottles and caps. (Almost everything here is screw-top)

Any help would be greatly appreciated, thanks!