I am a younger adult, but I have a disability, so I may be able to contribute my experiences, which I hope will be helpful and relevant to your mum's situation. I prefer a cylinder vacuum, for the sole reason that there is less weight to push around. All I have to do is to use the hose/tube which is far easier than having to push around the whole machine.
My vacuum cleaner is a Miele TT2000 Cat & Dog model, which I bought for £189 from John Lewis. You could probably shop around for a cheaper price on the internet if you want, but I prefer to buy from a reputable retailer.
My Miele has a 2000W motor, it is very easy to manoevre, and it has a retractable cable, which I find to be quite a useful feature. It uses bags, but again, I find that to be OK because it is easy and simple to use. It is quite compact and easy to store.
Not everyone prefers a cylinder, and not everyone wants to use a machine which uses disposable bags, but it works well for me, as my limited experience with a bagless cleaner was just messy and dirty and created more work.
I decided against a Dyson for a number of reasons. Firstly, their cylinders were more like some complex puzzle than a user-friendly storage solution, and their uprights are way too big and heavy for me to use. Secondly, a relative of mine has got through 3 Dyson uprights in the past 5 years, and found their customer support left a lot to be desired. Not to mention that their performance was not all it was cracked up to be, as the ads would have us believe. I know Dyson has its fans, and many customers are happy with their Dysons, but they don't produce any disabilty-friendly models, as far as I can tell.
The Miele suits me very well, not only is it easy to use, it is also very powerful and efficient.