What I put in my FAK might well be different from what you would assemble, because our training and experience probably differ, and we may well be hiking in different situations. In general, realize that much of what is needed can be improvised from other gear. Some things can't. I generally carry sterile dressing, some kind of tape, elastic (Ace) bandages, and modest painkillers like aspirin. Nowadays I also include at least a pair of nitrile disposable gloves. I always have bandaids in my wallet and a reasonably clean bandanna in my left rear pocket - that is the immediate FA gear for me.

I really like elastic bandages. Over the years, the most debilitating injury has usually been a wrenched knee or ankle. As long as you are sure no fracture is involved, wrap 'em up and keep on hiking.....

Standard, required statement - Get trained. Without training, the FAK is basically just so much junk. With training, you can do quite a lot even without any dedicated items at all.