Hi there orchidday...
Shoulder press should start with the handles at just above being in line with your shoulders.
I never use it though - I prefer dumbbell press, or even better, arnolds. Have you tried them? They're WONDERFUL, because they hit all three heads of the delts, instead of just the front heads. This helps make your shoulders look broad, instead of curling forward.
Standing lateral raises are a good idea before doing any other shoulder work.
Use a light weight (I only use 10 or 12 pounds after 3 years, this isn't a mass exercise) and pay attention to form. Imagine you are pouring VERY full pots of tea, and try to imagine you are leading a TINY little bit with your elbows, but only a smidge:
Grasp dumbbells in front of thighs. Bend over at hips slightly with knees bent.
With elbows slightly bent, raise upper arms to sides until elbows are shoulder height. Maintain elbows' height above or equal to wrists. Lower and repeat.
These are arnolds. You'll be able to use probably about double what you use for the laterals for the arnolds:
Grasp dumbbells; palms facing body, elbows flexed.
Raise dumbbells by extending elbows; abduct and internally rotate shoulders to straight arm position. Lower to original position and repeat.