I've seen that kind labelled as
Ruby Ball Cactus. You can learn more about it, here
https://home.howstuffworks.com/ruby-ball-cactus.htm
Colour isn't the main concern with Cacti. You need to make sure that you have the basic requirements right.
Cacti in general, can be kept on a windowsill. The best direction for them to receive sunlight is south. The next best direction is west.
You don't have to repot now. Spring is the best time to do it but, you can do it at other times throughout summer. I don't do it in autumn or winter. When you repot, you should use a pot that is either the same size or, only a little bigger than the current one. You don't need one that is a lot bigger. It is best to use an unglazed, clay pot because that lets water drain properly and prevents the soil staying damp. Damp soil causes rotting and is a quick way to kill a Cactus.
I noticed that you have the pot in a glass. That's helpful because it will collect water that runs out the bottom of the pot, when you water your plant. When that happens, you can lift the pot out, throw away the water and put the pot back in. Leaving the pot to stay in water that has already run out the bottom of it, will cause damp soil, something to be avoided.
Please update this thread to show your plant gets on, in the coming months. It's an attractive one.
