target minutes is especially bad in edge cases, but for most people, you are trying to optimize average case, not edge cases like this.
short version - always use fatigue first, with everyone on fairly fresh, and adjust from that as needed. generally speaking, there is no press team that should be using target minutes for the NT.
however, man and zone teams IMO can work better with target minutes, in particular circumstances. the default is always still fairly fresh depth chart, but that tends to work REALLY well if you have an even 10 man rotation - which generally speaking - you almost always have in press, but usually should NOT have in m2m or zone. m2m and zone coaches running straight 10 man rotations, when they shouldn't, is one of the most pervasive and most severe mistakes made in the game today - and it happens from the bottom all the way to the top.
when your 3rd best guard or big is significantly better than the 4th, you should be attempting to get a 3 man rotation the bulk of your minutes (3 guards, 3 bigs, whatever - you can do it at any 2 spots, sg/sf and sf/pf are decently common even though pg/sg and pf/c are the most common). this can be accomplished in a variety of ways, but sometimes, there is no way to do it with fatigue. if you have 2 even stamina starters, your backups will spend the large majority of their time playing together, which is what you are trying to avoid. a big stamina differential between the top 2 starters, especially with a higher sta backup, is ideal.
unlike fatigue, you can *always* use target minutes to set up a 3 man rotation. it just is less than ideal in other ways, and a lot of coaches will screw it up due to not being familiar, so i strongly recommend practicing minutes... not in the NT... if you are going to practice it. carry it into the NT when it works. i have been known to switch in and out of minutes during the NT, but i'm not sure i can in good faith recommend that to others. there is no question in my mind that it is required for full optimization for certain teams though, so keep it in mind for if you get good at minutes and are engaged with your team enough to safely make changes of that magnitude between NT games.
start by taking your teams where you really want a core 7-8 leading the squad, who you can't get enough time to in fatigue, and try minutes for them. you roughly want your total to be 180-220 or so, for the NT (its ok to go lower in the regular season for promise meeting purposes, but in the NT, you are usually trying to precisely control the whole shebang).
it is worth noting like that fatigue, if you don't fill out the bottom half of your depth chart, you can put yourself in a pretty bad way. do not use minutes (or fatigue, but especially minutes) without a robust depth chart. i am not a target minutes expert, i tend to play press where its grossly inappropriate, but i definitely see the value in it. hopefully this gives folks a little bit of a starting point and they can take it further than i have.
(edit) P.S. - make sure when you run a 3man rotation, you are deliberately controlling where the backups play when they are on the court together. its bad to have a 3rd man at the 2pf/c and a 4th man at the 3pf/c slots without 1) knowing how they will play together, and 2) if this is what you actually want.