What's the most economical way to digitally measure 240V mains voltage, current and power factor?
I used to design electricity meters so I'm biased. There's only one way to measure power (digitally) and that is to simultaneously sample the voltage and current waveforms at a reasonably high rate such as 1kSps or above. You multiply the v and i samples to get instantaneous power samples. You then average these power samples to get true average power i.e. the type of power that you are billed on: -



If you need to measure 3ph power see this link for the two wattmeter method

None of the above has to take into account power factor because PF is just a nice retrospective number that may be used for reducing a site's current and thus avoiding being billed for exceeding reactive power limits. In a household, this extra bit of the billing isn't applied as far as I know and in the UK it was only 100kW users and above who were encouraged to use PF correction to avoid the extra charge from electricity providers.

Let me reiterate 

POWER FACTOR HAS GOT NOTHING TO DO WITH PROPER AND ACCURATE POWER MEASUREMENT.

Why do you need to sample at 1kSps I hear someone say - reason - to avoid nyquist aliasing errors. yes the voltage is usually a pretty undistorted sinewave with minimal harmonics but not the current. Just think about the current taken by a bridge rectifier, smoothing capacitor and load: -



The power supply's smoothing capacitor only gets recharged at the top of the voltage cycle and, largely, the rest of the time no current is taken from the AC supply. It is for these circumstances that fairly rigorous  high speed sampling needs to be done.

Then ask yourself, given the bad shape of the current in households, does  RMS voltage, RMS current and trying to evaluate a meaningful power factor make any sense at all to power? 

No, of course not and so any device that does not measure power by averaging the result of the instantaneous multiplication of voltage and current is a fraud.

So, measure and calculate power properly and along the way you can calculate RMS voltage and RMS current - you could then divide the RMS numbers into the power number to give you a true measure of power factor BUT, you don't need to know PF at all if you want to check your bills.