JJ is quite right, of course, in respect to the power. They will not replace a mains vacuum but are ideal for small kitchen spills where it's too much bother to get the mains vacuum and better than a dustpan and brush. We also use ours in the caravan just for keeping it tidy.
Cleaning the car is always done with the mains vacuum.
black and decker dustbuster extreme.excellent suction power ive had a few small vacs this is the best ive ever had i got this from home bargins around £27.00
It's going to be mainly used for cleaning the stairs. Going on the comments, I think a corded hand-held one might be the better option, can you get them?
I'll second JJ - for jobs like that you must have mains power.
Incidentally, we have the older version of this which is a conventional cleaner but converts to a cylinder for stairs etc. we've had ours for several years now, with no problems.
I have some arthritic problems and if you can afford it this is the best vacuum I have ever had: http://www.dyson.co.uk/vacuum-cleaners/cordless/dc59/digital-slim.aspx
I use it all the time and therefore I never run out of power, little and often is the was to go and it is brilliant for the stairs in the short mode, and then quick change and it is a fantastic cobweb eliminator and light enough for me to manage with limited grip in both hands.