Well, Modern alchemy in an esoteric sense is about finding a philosophy of personal change. As far as a more traditional, 'chemicals in beakers bubbling over fire' kind of alchemy, then you would be looking for chemistry equipment as that is what alchemy essentially was.
For the Esoteric approach, bookshelves, maybe a desk, and a comphy chair are all you really need. And maybe a few shelves or a side table for a place to put a rock collection if you start one. basically you just want it to be a place where you can put your books and keep your thoughts.
For the more literal approach, look online for home scientific lab equipment. beakers/phials/test tubes, stoppers, bunsen burners, glass and plastic pipes of varying sizes and shapes, a functioning sink/water supply, safety ventilation, fire suppression (type b or c for chemical fires), likely a fridge and/or freezer, sample storage containers, oils safe for storing volatile minerals to keep them away from oxygen and water, maybe some fun stuff like liquid nitrogen and dry ice, a certified emergency eye-wash station and emergency shower, Lab clothing (Coat, gloves, etc) appropriately rated for the materials you plan on working with, co2 and carbon monoxide detectors, some sort of high-definition weighing scale, and a land-line emergency phone.
There are more tools I am sure, that might be more specialized to specific materials and safety reuirements. Like a variety of microscopes with a range of styles and uses. or, if you want to go a little less modern, just hunt down old-school equivalents.