When I begin applying rosin, I tend to apply a bit more at the tip than at the frog and mid-section. Then, I will test the bow on all strings while the rosin application may still be on the light side. This testing is with long, sustained strokes as well as spiccato, martele and chord playing. If needed, I will apply more to the appropriate places. Finally, I'll lightly wipe the hair with a cloth so as to remove the loosest particles and smooth things out a bit.
As a general rule, I am partial to playing with less rosin than more. There are numerous disadvantages in having too thick a layer on your bow hair.
I use synthetic core A-D-G and a steel E, as do most violin and viola players these days. I have been very pleased with Bernardel over the years. However, there are most certainly other worthy brands in our catalog, and I recommend testing them. Try to remove as much or your old rosin as you can before applying the new brand.