Great news about the extra room. You'll be so glad you tried it! You can use the same tanks for both 120 and 35mm film, but different reels. If you have a two reel 35mm tank, it'll take one reel of 120 film. I just keep my times and temps the same for both. I prefer the stainless steel tanks, better agitation, and the plastic tanks can start to absorb chemicals over time. But the stainless reels take some practice to get loaded up. Just sacrifice a roll of film to try it with the light on. The 120 reels are much easier. There is a huge development chart at Digitaltruth.com with all sorts of developer/film combinations. I think a good place to start is Tri-x or HP5 in Kodak D-76. When you get comfortable then playing around with different developers and films will be easy. Tri-x and HP5 are fairly forgiving when it comes to slight temperature changes. etc. You want your first rolls to come out!
The best thing about doing your own developing is the control you have to work the way you want to. Rather than be at the mercy of the lab, you can use Rodinal, or Pyro, or some home brew that you read about and can experiment with different materials until you find something that fits your vision.
Yes you can develop both 35mm and medium format with the same chemicals and equipment. A one reel medium format tank will also hold two 35mm reels. The developing times may be slightly different between 35mm and medium format depending on the brand of film, but is usually not that much different. Most enlargers will handle both 35mm and medium format up to about 6x7.
For chemicals, I would start out trying what is readily available in your area first. Everyone has their own opinion about what film / developer combo is the best for them, so I would say experiment with a few untill you find one that you like using and then learn everything you can about using it.