Some of the smaller species will not outgrow their welcome in a modest size greenhouse. Plants like Puna bonniae or Austrocylindropuntia verschaffeldtii will stay small, even after years. The same goes for Micropuntia's. Also Tephrocacti are not the fastest grower, although they will get quite big when given time.
How different is it for the true Opuntia's. Most species will happly fill a big bowl of 60 cm diameter, and even that will not be enough in the long run. Pads after pads will be made, and the grower looks at his plants thinking when they will stop growing. They won't. But don't worry. Taking cuttings is easy. And happely growing Opuntia's also means more flowers.
Glochids can be a problem, so be sure to handle your plants with care. Children and clochids are not a good combination. Regular spines can be removed, but quite a few have barbed spines, not to mention the spines of Cylindropuntia's. I saw during my first visit to the USA in 1997 that a teenager was taken to the hospital in shock after coming in contact with a vicious Cylindropuntia. These are always at the back of my bench for a very good reason.
Some species can be (very) invasive, depending on your location. Often these are larger growing plants. Species like basilaris or aurea won't be a problem quickly. Their demands are just too high.
In The Netherlands, the chances of any Opuntia running wild in the landscape are zero. We lack the soil and climate to be favourable for our beloved plants. If not on specially prepared soil on a favourable spot, fungus and bacteria will kill the plant swiftly