As with many hobbies and pastimes there are some essential things you need and then there are some bits of kit that are useful but not strictly necessary. You need a lot more equipment for brewing mashes than you do brewing from a kit.
The bare minimum equipment for brewing from a kit would be a large kettle, long handled spoon, fermenting vessel, airlock and bung, syphon tube, bottles, caps and capper and sanitizer/cleaner.
When brewing from malt extract, add to the above with a large boiling pan and a sparge bag. When brewing mashes you will also need a water boiler and sparger. A hydrometer and thermometer are not essential for even full mash brewing, but are very worthwhile investments