I do warm up sets before the main sets (I also do a full shoulder routine before every day that uses shoulders - so chest and shoulders day for me, but I would include it on most days for you as how you have the routine structured). This is it here, before I did it I would get aching shoulder a lot from a previous RC injury, but since I get hardly anything
Just before i go on about the warm ups, you mentioned stretching. IMO you shouldnt stretch before working out as stretching a cold muscle can increase the likely hood of a pull or a tear. Stretch afterwards when there is warm blood flowing through the muscles.
Warm ups can be light aerobics to get the flood flowing and the warm the blood up (personally i dont do this very often, even though i know i should), or specific sets for theat muscle group. I do warm up sets for the firts exercise for any muscle group. For instance if i was doing chest and shoulder I would do a warm up set before the first chest exercise, then the remainder of sets without warm up sets (as the muscle will be plenty warm). If my next exercise was shoulder press then i wouldnt warm up as the anterior delts would be warm from the chest pressing. i may however do a specific warm up set for the lateral delts and/or rear delts if i was also working them as they wouldnt have been worked as directly.
To know how much weight to lift on a warm up set (again I'll use bench as an example) for sets of 10 @ 100kg, I would do 10-15 with just the bar, then about 5 or 6 at 40kg, 4 or 5 at 50-60kg then 2-3 at say 60-75kg. The idea is you want to get the CNS ready and the muscles warm with fatiging them altogether.
There are loads of benefits to warming up mate, including
(taken from The Warm Up - How To Warm Up Before Exercise
•Increased Muscle Temperature - The temperature increases within muscles that are used during a warm-up routine. A warmed muscle both contracts more forcefully and relaxes more quickly. In this way both speed and strength can be enhanced. Also, the probability of overstretching a muscle and causing injury is far less.
•Increased Body Temperature - This improves muscle elasticity, also reducing the risk of strains and pulls.
•Blood Vessels Dilate - This reduces the resistance to blood flow and lower stress on the heart.
•Improve Efficient Cooling - By activating the heat-dissipation mechanisms in the body (efficient sweating) an athlete can cool efficiently and help prevent overheating early in the event or race.
•Increased Blood Temperature - The temperature of blood increases as it travels through the muscles. As blood temperature rises, the binding of oxygen to hemoglobin weakens so oxygen is more readily available to working muscles, which may improve endurance.
•Improved Range of Motion - The range of motion around a joint is increased.
•Hormonal Changes - Your body increases its production of various hormones responsible for regulating energy production. During warm-up this balance of hormones makes more carbohydrates and fatty acids available for energy production.
•Mental Preparation - The warm-up is also a good time to mentally prepare for an event by clearing the mind, increasing focus, reviewing skills and strategy. Positive imagery can also relax the athlete and build concentration
hope this helps