I’m a cleaner and I wouldn’t give you tuppence for a Henry, they are top heavy, not at all easy to store and the suction is rubbish. The only good thing about them is they are little work horses and will pick up anything.
If you get a Dyson then go for a ball one as they are considerably lighter and easier to manoeuvre - I have an animal one at home and wouldn’t swap it for anything. All Dysons can appear flimsy when you first start using them but they are sturdier than they seem.
The mini balls are good for portability, I use one every day for work, getting it in and out of my car and into different houses and on different floors and it’s fab. They don’t have quite as much suction as their big brother and the bin is a lot smaller but I don’t find it a problem.
I don’t think the rechargeable Dysons are any good unless for extremely light use and they are overpriced in my opinion.
Never tried a Shark but I’ve heard good things about the suction. I don’t see the point of the removable section but that might just be me.
If you get a Miele then make sure you get one with a wheeled head on it - without it they are very hard to push on some floors. They are quiet vacuums but I don’t find them easy to use.
Personally I love Dysons and wouldn’t consider anything else, I’d definitely never get a cylinder vacuum if you have a back problem as they’re far harder on your back in my experience. Try as many different ones as you can - ask anyone who will let you try their vacuum! lol