There isn't necessarily a "correct" length to aim for with a looping track — that's why you'll find different game tracks have different lengths!
Instead, you may want to go research some games that have a similar style and audio feel to what you want. Look up their soundtrack online and check the lengths of the tracks they use, or time the repeats yourself with a stopwatch in your own play or while watching a Let's Play recording.
Do this also for a game or two you find '"too repetitive" for your taste, musically, and compare. That gives you a lower bound to aim above.
You may also want to consider commissioning a short looping track with "stems" — multiple separate layers that you can fade in and out over a longer period to break up the repetition, or signal changes in gameplay state like boss waves. This can make a short loop seem much longer and less repetitive.
In my TOJam 2016 game Last One Standing, the sound designer I worked with, David Vitas, split the single BGM track into two layers: one with just the percussion, and one with the melody. In-game, I play both in sync, but vary the volume of the melody with the intensity of action, punctuating moments of rest in the gameplay with little drum solos. Because it's reacting to the gameplay, it rarely loops exactly the same way twice in a row, making it feel much longer and more dynamic, even from a very simple basis. (In that case, it was about a 90 second loop)