Most are powered usually by a USB cable from the laptop. This can of course be plugged into any USB power source.
IMO those with one or two large fans are better than those with many smaller fans. The large fans move more air, make less noise, and generally last longer.
I'd also suggest one with an aluminium grid on which the laptop sits rather than plastic. A plastic grid retains more heat than an aluminium one, so you're drawing warmer air in - not something you want.
Generally you get what you pay for, the cheaper ones are probably best avoided.