Properly fitted bra is the one with the band size tight enough to keep the bra in one place, however it has to be comfortable enough to move and sit with arms either held down or high up. Also it can't ride up in the back, which is caused by bra band being too loose and bra straps fastened too much.
In general you should be able to slide the hand behind the band on the back, but shouldn't be able too pull the band away from the flesh.
When buying a bra, get the bra with the band fitting you on the loosest adjustmeant. The smaller adjustmeants are for use later, when after a while band fabric stretches and you will need to make it tighter.
If the bra band is too tight on the biggest adjustmeant, buy a bra with band that is one size larger. It will require to switch the cup one size down to remain the same cup size.