Hello everyone, having done a couple of experiments on that same subject during the past couple of weeks, I 'd like to add my two cents in the conversation.
Do note that:
a) I'm still playing on the 43.05 version so there might be some differences with the most current one
b) I'm using Dwarf Therapist to monitor my dwarves.
Experiment 1: Wrestling training before weapon training.
I managed to get my initial dwarves at level 10 in both wrestling and armor (they started with 5 at armor) when a wereantelope attacked and pretty much killed them all. Their equipment at that point was a full set of iron armor (breastplate,mail,helm,high boots, gauntlets, greaves and cloak). As you can tell , my results were quite disappointing, however they are not conclusive.
Experiment 2: Weapons and armor training.
Using the same starting skillset (5 at armor), I gave each of my initial dwarves a full set of iron armor plus a weapon of their choice and let them train. When they all reached 20 at their weapon skill, I also gave them a shield. At that point, their armor skill was between 10 and 15, wrestling was ~ 15-18 and most of them had already reached their limit on strength, agility, toughness etc.
At about the same time I started training a second squad, using the same training plan with one exception, I would give them shields when they all had reached 20 at weapon and 15 at Armor.
Conclusions:
1) Focusing on wrestling seems to be inefficient as a training method. It seems to perform worse as an attacking skill than weapon skills of the same level and most importantly dwarves will train it automatically when sparring with their weapons anyway. As far as attribute training is concerned, both wrestling/weapon training seem to be equally effective.
2) Shield is probably the easiest/fastest skill to train. Both of my squads achieved a skill level of at least 15 by the time they got around 15/18 (from 10 and 15 respectively) at Armor. From experience on previous fortresses, giving them shields from the start, seems to result in very slow armor training. I suspect this is due to dwarves getting too good with shields and blocking most of the incoming blows with them instead of using their armor.
3) There have been no injuries in any of these 3 squads during training. However, on a previous (kobold) fortress, I did have a couple of deaths during training but I'm not sure if it was due to sparring or because they got into a fight among themselves (I think it was always one particular kobold involved).