Your studio can be as simple or as expansive as you have funds and the time/space for. I started my pottery hobby without anything taking classes at my local art studio. This is a great way to start and meet the people that will become your community going forward.
Over time and with the help of generous ceramic enthusiasts, I have built my own small space to work. It gets better little by little and is coming along nicely if I do say so myself. Included in my studio (shed out back), I have:
Half of my old kitchen table mounted to the wall
A "free to me" kiln that I was fortunate enough to find on FB Marketplace - the previous owner was so nice and took great care of it. She taught me how to use it and included some kiln hardware to get me started!
A $40 Shimpo RK-2 wheel from the 1970's I think that needed a little love but still has a huge amount of torque (another FB Marketplace find)
A 2nd work station for drying out wet clay and wedging - this is also where I "mount" my Shimpo Mini slab roller
Shimpo Mini Slab Roller - love this thing!
Scott Super Duper Clay Gun extruder for making handles and hollow forms
Additionally, I have a wide variety of tools, cookie cutters, rolling pins, texture gizmos, and whatever else I can find that might look cool in clay. The important takeaway is that none of this cost me very much, space is really your limiting factor if you are willing to search FB Marketplace and similar sites and then drive to pick things up.
My last hurdle to figure out heating for the shed in winter. As I live in central NJ, it's freezing several months of the year and it makes for a rough time working with clay and water. Right now I am using a small propane heater but need a better solution.
Two other considerations are water and wastewater. Water is a requirement for clay work and while running (hot & cold) water would be awesome, I can manage with bring water out to the shed. The larger challenge is the wastewater produced from clay working. Clay is not something you want poured into your drains so you need to fins an alternative way to deal with it. If you have a sink in your workshop, you can install a clay trap/separator that removes it from your water before it goes into the sewer lines. For me, I use a 5 gallon settling bucket to separate the water and clay before I dispose of the water from the top of the bucket. The remaining clay is they repurposed and rework in to useable clay.
Whatever you have, enjoy the process...