There is no such thing as the best progression method. Of course depending on your individual goal and situation one can be better than the other. However, there are some methods and rules that, when applied can get you closer to your goals.
Strength and Skill Training
When it comes to building strength, methods used are going to be almost the same as in the skill training; Strength is a skill after all.
Train when you’re fresh/Don’t train if you’re tired
Train as often as you can.
Never train until failure
Train with a perfect form
Rest a lot
Some of them may look like total opposites but it all comes down to real-life application.
One of the best methods that obey all the rules is Greasing the Groove (GTG).
I’ve read about it in Pavel’s Tsatsouline “Naked Warrior” and thanks to this method I’ve learned the pistol squat, one arm push-up and definitely speeded up my first muscle-up.
To do the GTG properly, you choose a move that you’re currently working at. And every time you do something you perform that specific move. Here is how it would look like for overhead press. Every time you go to the kitchen you stop at your home-gym pick a relatively heavy weight ( that you can lift with an effort but without an injury risk) and do 5reps. Or another more life-applicable example. Montage a pull-up bar at the entrance to your bedroom. Every time you go in or out do few of your hardest pull-up variation.
This way you may end up doing 10,20 or even more sets of the movement without actually feeling tired.
The downside of that method is that it can be tricky to utilize for some of the more powerlifting movements and that it may interfere with your workout regiment.
Traditional Strength Training
Another simple way to make the fast strength gain is good old-fashion strength training.
Meaning, heavy loads/progression, a lot of sets during the week, long rest periods.
The important thing here is to pick only a few lifts that you want to focus on the most. Start with a bit lighter weight to allow for future progress. If you start to heavily then you’re much more likely to burn out faster. And if your main goal is strength then doing fewer sets in one workout with multiple workouts per week is better than fewer workouts with more sets.
This is something to utilize not only in strength training exclusively but also in your hypertrophy workouts. To make it as simple as it can be, you start a cycle with a weight that you can do 10 reps but perform only 5-6reps x2-3sets. Every time you perform that lift you either add 2.5-5kg or a rep to your sets. After a few weeks, after a workout that you achieved new PR, you drop the weight to your 2nd workout of that cycle and repeat. This way you will allow your body to recover properly and after another few weeks get a new PR. Ideally, one cycle is something between 8-16 training sessions. And yeah there are plenty cycles variations but the simple the easier to track.
There you go my top methods to speed up those strengths gains.