One technique which may help is to select your flight path vector (FPV) on your PFD and note the degrees, (for example 3.0 degrees) and use that as a default tilt starting point for climb. 5 degrees is OK for takeoff but too high for an established climb. Leaving the tilt there will not give the complete picture. Use the enroute park position (tilt so as to leave a green band of ground return at the far edge of the ND) and vary the range from 40 to 80 during climb adjusting the enroute park picture to form a strategic plan -left or right or left then right then left etc. Adjust the stategic plan to a tactical maneuver when within 40 NM of the weather cells. Try to deviate upwind for turbulence avoidance.
Someone brought up the Collins 2100. For further study, when you have some extra time, Google WXR 2100 and select the smartcockpit 222 page PDF operator manual. I realize you don't have this type of radar on board, but just skim through it and look at the graphics and read about radar energy, reflectivity, beam width, and gain adjustment to get the gist of what the 2100 is doing. With your manual radar you are trying to form a mental picture of the weather threat, just like the 2100 is doing electronically. Good luck.