Strict Press Vs. Push Press Grip

The Strict Barbell Press

It's one of the greatest exercises for overhead strength development. It allows you to move a lot of weight over a large range of motion.
When you're doing it, make sure your wrists aren't overextended. Why? Because it'll either keep you from lifting the weight or it'll place tremendous strain on your wrists.

The Barbell Push Press

It has the ability to let you press MORE weight, although due to the nature of the exercise, the range of motion is shorter. Because of the hip drive it becomes more of a full body exercise, which is fantastic for overall strength development. And if you add some slow negatives from the top of each rep it can have some carryover to your strict press.
Depending on your level of flexibility you may find you struggle having a closed grip in a front rack position (with your elbows up in front of the bar). The best way to get the most out of this exercise is to relax your grip and let your body do the work.
If you've never done Olympic lifting before, it'll be harder to adjust your technique and allow the hips do the work rather than your arms, but it's definitely worth the time investment and it'll get your numbers up.