I could buy type-B USB OTG host hub like this (4th selection) and type-B female/type-C male. But do I need some special adapter which supports OTG? Or maybe it's better to buy type-C OTG host hub?
It is better to use type-C
As more devices are moving to type-C and you can phase out your adapter for type-B over time.
Type-C also has more capabilities and you will be handicapped later on by converting from B to C. https://en.wikipedia.org/wiki/USB-C
Your HUB does not need to specify OTG as it a standard that is addopted by the device your are attaching it to (IE your smartphone). https://en.wikipedia.org/wiki/USB_On-The-Go
Here is a USB-C hub that has worked very well for me across desktop, laptop, and smartphone: https://smile.amazon.com/gp/product/B07GDHD3VC/ref=ppx_yo_dt_b_asin_title_o04_s00?ie=UTF8&psc=1
Edit to answer comment: Your first question is answered above. Your second question is answered below.
Here is an image of what you are likely to find inside the adapter: https://images.app.goo.gl/AVwQqKQCk6SfeSMj7 The unused pin you see is used to sense whether your phone should act as the host or the device. When it acts as the host you are in the OTG mode.
You could purchase a USB-B to A OTG adapter and a USB-A to C adapter but there is no guarantee that your older devices will support this. If you want to make sure both devices work, you could get 2 OTG adapters: one from B to A and one from C to A, and then use a USB-A hub.