I use a Dyson V8 which I think is great. As with all hand-helds it depends what you want to clean. It cleans admirably well on the "normal" setting, but the high setting will suck up difficult stuff (but greatly shortens the charge). There is definitely enough charge for me to hoover 3 bedrooms, two bathrooms, the landing, stairs, hallway, living room, dining room and kitchen (none of these are huge rooms though).
Battery isn't removable, and the charging unit is mains powered. I mounted mine under the stairs and it works nicely.
Only downside is the things are expensive. On the upside, although after 3 years of use, the trigger stopped working. Dyson repaired it for free (well just sent out a new handset really after looking at the old one), so very happy with customer service.
The filter does need cleaning regularly and it needs emptying before it is stuffed full. I did buy a couple of extra filters so that if one is drying, I can still use the vacuum.