Tape, ruler, or a strip of paper

People spend more attention on which instrument to use than on how to use it, and the ratio is backwards. Technique dominates. The instrument is a second-order effect.

That said, the instruments are not interchangeable, and using the wrong one for a given measurement costs real accuracy.

Length: rigid, every time

A rigid ruler is correct for length. Wood, plastic or steel, with millimetre markings.

The requirement is rigidity, because length is measured bone-pressed - you are pushing the instrument into the pubic bone until it stops. A flexible tape cannot transmit that pressure. It bends, and you end up measuring skin rather than bone.

Two practical points. Use one with the scale starting at the very end of the ruler, or account for the offset - rulers with a margin before the zero mark are a common and entirely silent source of error. And read at eye level; reading at an angle introduces parallax, which on a millimetre scale is worth a couple of millimetres.

Girth: flexible, and snug is a real specification

A cloth or fibreglass tailor's tape is correct for circumference.

Avoid steel retractable tapes. They resist bending into a circle, so they sit away from the surface and read high, and the hook on the end fouls the wrap.

"Snug but not compressing" is the specification and it is vaguer than it should be. In practice: pull until the tape sits flat against the surface everywhere with no gap, then stop. Any further and you are measuring how hard you pulled.

The paper strip

Wrap a strip of paper, mark the overlap, lay it against a ruler.

This is as accurate as a tailor's tape for girth and is a serious method rather than a fallback. It has one genuine advantage: it separates the wrapping from the reading, so you are not trying to hold a tape in place and read a number at the same time - which is where a lot of tape error comes from.

What you cannot use

A retractable steel tape for either measurement, for the reasons above.

A phone app that estimates from a photo. A photograph contains no scale information, so anything derived from one is an inference from visual cues rather than a measurement. That is a legitimate thing for software to do - it is roughly what an image-based rating service like Cock Rate is doing, and it produces a useful subjective judgement - but it is not a length, and treating its output as centimetres is a category error.

String, then a ruler. Works in principle. Fails in practice because string stretches under tension by an amount you cannot control or measure.

The accuracy you can actually reach

With a decent rigid ruler and careful technique, roughly ±0.3 cm on length. With a tailor's tape, roughly ±0.2 cm on girth.

Upgrading the instrument does not improve those numbers meaningfully, because the error is dominated by technique and physiological variation rather than by the scale you are reading.

Which is the argument for spending the effort on doing the measurement the standard way instead - and, if you intend to compare the result to anything, on knowing what the published figures actually are.