I support most of what is posted above; however, my own view is that there are many practices that may or not be helpful in their own right (e.g., stretching, warm-ups, Qi-gong, zhan zhuang, dim mak, strength training, aerobics, meditation), but which are not integral to some versions of Taijiquan. If you try to study such versions only from those viewpoints, you may run the risk of missing something important.
As far as I know, practicing condensing breathing during the form the Association teaches would be detrimental, at least at the beginning and intermediate levels. For a few years, I used to practice specific breathing techniques to match the movements, but ceased to to so once I made up my mind what type of Taijiquan to study. At least for me, this was definitely the correct decision.
If you practice the Association's Taijiquan (or the many similar versions with like lineage and/or principles), neither the breath, nor the Qi should be manipulated beyond a very minor level: i.e., keep the breathing long, deep, and continuous and generally sink the Qi to the Dantian.
It is definitely wrong to chase unusual Qi sensations, either to enhance them or eliminate them. In this sense, there is much more emphasis on what not to do than on what to do, because the goal is to be supremely natural and let the body processes calibrate themselves.
As for Shen, Jing, and Qi, these are difficult concepts to discuss succinctly, but I would say that most of what is needed within the Association's Taiijiquan is covered within the Ten Essentials. In other words, if you embody the Ten Essentials, those three concepts will largely take care of themselves and do not need special, dedicated techniques. Your body systems know what to do if you treat them right and do not interfere.
As you evaluate what type of Taijiquan suits you best, you may want to keep in mind that simplicity and complexity are on a different axis than shallowness and depth. Also, some things are often presented as emblematic of Taijiquan (e.g., extraordinary use of Qi) that are better thought of as the common property of all Chinese wushu and not particularly distinctive of Taijiquan.