Following are excerpts from Eddie Kowacz’ training logs on push ups. I won’t change or add much. They are pretty self explanatory.

First is the Speed Pushup

“This is not your everyday push up that is done in a slow and grinding fashion. These are called ‘speed push ups’ and for a reason. They are done in an EXPLOSIVE, RAPID MANNER. The faster you do these the more benefit you will receive. I use a 3/4 range of motion, which means I do not lock out my elbows. The starting position to be used for this drill can be either at the top at full extension or on the bottom with the chest touching the ground. Once I decided which starting position I would use, I watch the clock and time myself for the prescribed number of reps.

Here is how you can calculate your optimal rep count. Test yourself for a max number of speed push ups you can do and train with 50% of that number. Go for 15, 30, 45, or, the maximum of 60 sec. I never saw the need to go over 60 sec. because at that point I was already over 100 reps and the drill started to lose its effectiveness.
The number of sets recommended to start with is 3-5 and none are taken to max. To get the full benefit with this program I would also recommend that it be done a minimum of 3 times a week. Start out slow if you are new to this drill and before you know it you will see the numbers climb in both sets and reps. Remember, DON’T MAX OUT ON REPS!”

The next is Weighted Pushups

“For the next few months I’m shifting my focus from Overhead Pressing to Weighted Push ups. Based on my previous training (years) I’ll be able to maintain most of my overhead strength using just the Jumpstretch green bands. I’ll also do some high rep endurance overhead work using either the minis or the purple bands. Of course, it’ll all be 2 arm work since I never do any 1 arm presses. I’ve never had a 1 arm pressing workout and most likely never will.

“About the push up reps with weight vest,  I think that it’s just a matter of being different as opposed to being better. However, it will still boil down to what you are able to handle once you move up to 80 lbs (or more). IMO, you should be able to handle 8 x 3 or even 10 x 3 right off the bat with the 20 lb increase, using more or less the same period of rest between sets.
If you find yourself struggling on set 8 and want to do 10 sets increase the rest period by 50% or so and bang out the last 2 sets.
I’ve always preferred set and rep schemes of 3’s and 5’s whether it’s 8 x 3, 12 x 3, 5 x 3, 3 x 5, etc, etc.”

Examples from training log-

Weighted Pushups done with 45 lb plate for 3 sets of 20.

Weighted Elevated Pushups done using handles + 100 lb plate for 6 sets of 5 reps.

Weighted Pushups done on handles wearing 40 lb vest + 1 mini-band for 5×5.

 Strength training is all about the weight that’s used and not about the implement that’s used.