In the end you would need to decide what works in your design but based on the information provide I would do the following:

8mm screws (there is still plenty of material left in the 15mm plate). 8mm are tightened to a higher torque so your clamping force on the joint will be much higher. Plus the heads are larger so make better contact with the piece they join to. You need to check the other material can accommodate the size of the head if using cap heads and they are countersunk.

Anything deeper than about the 1.5 x D for threads does not improve the joint. 1.5 x 8 is 12 so drill min 20 and tap to min 14 to allow you to use M8 with 12 mm engagement.. If you have a bottom tap you can drill a bit shallower but make sure you can tap enough whole threads.

For 125mm width I would choose 3 screws if the design allows. We could go into joint calculations and stress triangles but I’m not sensing you want to go there so at least 2 and ideally 3. One would be in the centre and the outer 2 would be set in around 15mm or so from the edge.