There are exceptions, but in general most tuning meters are set to read in equal temperament, which is great for orchestral applications, and the like. In other words, if playing around the circle of fifths, in all twelve keys, on a fully chromatic instrument is in your plans, then perhaps a typical tuning meter could be a useful reference.
However, an acoustically sweeter tuning is known as “just” intonation, and, for instance, when it comes to ITM, that’s what I tune to. Some tuning meters include a feature, to provide a reference tone, often an A at 440Hz, but I do it the old fashioned way, by striking a tuning fork, then getting that reference tone into my ears, then tuning the same tone on my flute to that tone, and then tuning the other six tones of a diatonic scale, such that they are then acoustically sweet to the original reference tone.
Basically, this is a typical part of “classical” technique, where instead of picking up an instrument and going straight for a tune, one first spends a few moments at getting tuned up, whether equal or just, and then after that, one applies that tuning to their choice of tune, as the acid test, so to speak. At first, spending some warm up time at tuning could be something less than fun, but eventually one’s ears, and corresponding embouchure tuning reflexes, become sharper, faster, and, more importantly, more accurate. The real benefit, here, beyond being in tune, is in gaining an ability to tune to other players, instantly.
Yes, it’s work, but the benefits are quite real.