IMHO with the big strength lifts that have an eccentric phase PRECEDING the concentric (squat, bench, front squat for example) you should learn to do the eccentric phase fairly slowly. DO NOT COUNT but it should take you about 3 seconds.
At first your results will be lower when training this way... meaning that you will likely lift less weight. But over the long run it has many many benefits.
First that eccentric emphasis will give you more strength gains. It will also improve your technique and precision as well as you capacity to hold proper positions under heavy loads. It is also safer on the tendons which will give you the chance to go heavy more often and also avoid injuries more easily.
HOWEVER studies have shown that a faster eccentric and rapid turnaround increases power production. So being able to "turn it on" and do a more rapid eccentric to utilize the stretch reflex is a skill that should be trained too.
I now believe that it is best to do most of your heavy lifting with a slower eccentric, trying NOT to use the stretch reflex (yes the rapid eccentrics lead to a greater power production but not because the muscles are producing more force: because the stretch reflex contributes more) so that the actual contraction of the muscle produce most of the force.
But use short blocks of training where you train your capacity to use the stretch reflex.
A 9 week blocks would have two 3-week blocks (6 weeks) where you do the eccentric slower and one 3-weeks block when you train to use the stretch reflex.
Or you could use a mixed method where you do a set of 3 reps as follow:
Rep 1: slow eccentric/pause/hard push concentric
Rep 2: more rapid (still controlled) eccentric/pause/hard push concentric
Rep 3: more rapid (still controlled) eccentric/no pause-quick turnaround/hard push concentric
But that second approach should only be used once you have spent some time with more controlled eccentrics.
As for "speed work" I don't use it that much anymore. For building strength I'm not entirely convinced of it's value. I think that most people do not use it properly anyway and I think that it works only for a small portion of the population.