Well, back to the original question:
Voltage and phase MUST be measured along with current to produce an accurate reading. Otherwise you will be including reactive power along with the real power and you only have an interest in real power.
The power company's glass bubble meter uses a mechanical, yet surprisingly accurate mechanism that inherently takes into account voltage, current, and phase angle. Pretty neat, actually. In fact a digital device has to be well-designed and a bit complicated to approach the effectiveness of the bubble.
You can manually read the dials to find you consumption day-by-day, and read you power company's KWH cost to figure out what you use over a fixed time period.
There's a device called a "KILL-A-WATT" meter that Harbor Freight Tools sells now. These are quite nifty. They'll measure the consumption of anything you can plug into a 110V outlet. It'll show real power consumption, power factor, total KWH consumed since it was reset, just about anything you could want. This may even be more helpful than a "whole house" meter because that would not clearly spell out what each device costs. Well, the KILL-A-WATT can't measure your room lights that don't plug in, but then a 100W bulb pretty much takes 100W, doesn't it?
I've measured my PC and monitor. IIRC that thing was well over 200W, pretty hefty cost being left on all the time.