Sian I have Arundo Donax ( Giant Reed Grass) to give privacy in one part of my garden. It can grow up to 8 metres in 10 yrs if you let it. In 13 years I haven't found it invasive and you can remove any unwanted new shoots that appear. It is easy to snap off any that get too big at the base, I have fun doing that.
Far easier to control than either of my bamboo.
The hollow stems/ canes are useful for all sorts, I have them as runner bean supports. Friends had some from me to use as a roof on a pergola.
It does say semi- hardy but it's lived fine in Yorkshire on clay.
Gembo I had a Eucalyptus at my previous house and I kept it small about 6 feet, so it maintained its young leaves and interesting colour I didn't have a problem with it getting huge. Only problem I had was I was overly enthusiastic one year, pruned it too much and it died. It did say you cut almost to base and it would recover