I have had a vax cordless since moving house last year but the rotating head gets clogged up with hair. And I'm looking for something more powerful to do all the carpet upstairs, downstairs is all wooden floor. The cordless is fine for a quick scoot round picking up crumbs.
So something that can deal with hair and has quite a long lead but isn't too expensive.
I would also recommend a Henry. I've had a number of much more expensive vacuum cleaners in the past but am really impressed with the Henry. It's got excellent suction and is great on both hard wood and carpets. My cleaner is also considering swapping her Gtech for 1 since I've had mine.
I got it because it's very light and I have joint problems, but it's brilliant on hair (mine and the dog's) because it's cordless, I'm far more inclined to use it because it's so easy. It's good on hard floors, too.
We have the Henry Xtra HVX200-11 with the extra tools. It's proving much better than the Dysons, Miele and Sebo that we've had previously. We have 4 storeys, dogs and teenagers so all our vacuum cleaners get well used!