RE: training chest with shoulders
It is only shoulder pressing excercises that will suffer (or ohp, military etc) if you do them after chest. Excercises intended to hit the lateral and posterior delts, such as side and bent over raises will not be affected as they do not involve triceps (nor do front raises which hit the anterior delts) - However some people argue that beginners should not be doing isolation excercises on shoulders.
If I do OHP before bench my bench is not affected, however if I do bench first my OHP will not be as good - not sure why this is but give it a go. Make OHP your first excericse on shoulder/chest and tri day and see how you get on!