From the description you have given us, it sounds like the joint that is clicking is your AC joint. It is located on top of the shoulder where the clavicle meets the scapula, a search in google will give decent diagrams and descriptions. A simple way to confirm this would be to palpate this joint during the previous described motion and see if it is in fact the joint responsible for the clicking.
Repetitive clicking can be a sign of and may lead to joint dysfunciton down the road. One thing I would suggest is to never perform lateral dumbell raises in the above described mannor (thumbs down). It puts too much stress on the AC joint and the sensitive underneath. There are plenty of safe exercises out there to target specific muscles without risking injury.
As far as weightlifting goes, I would play it conservatively. Powerlifting is by no means the most healthy choice of exercise as it pushes our body's structure to its limits and usually beyond. In my yonger days I was a bodybuilder myself and had sustained several injuries due to overlifting, too much weight, poor lifting mechanics, etc. I would advise perfect to near-perfect form when lifting as this will minimize any potential injury and maximize the effects of the exercise.
To see a Physio or to not to see a Physio, that is the question... There are some who will say that if there is no pain then no, you absolutely do not need to see a Physio for this problem. I am of the philosophy that an ounce of prevention is worth a pound of cure. Therefore, it may not be a bad idea to seek some professional help regarding your shoulder and neck. A Physio skilled in musculoskeletal dysfunctions and who can identify biomechanical and muscular imbalances, may be invaluable in assisting you design an appropriate routine of safe exercises and ones to avoid. Good luck