To the subject of applying for SOLDIER, I know that a person could be scouted and brought in by the Turks. It also makes sense to say that there are probably countless numbers of people filling out applications to join SOLDIER and become heros. Best way would be to accept the most qualified candidates and make the rest of the willing applicants into grunts, allowing Shinra to then pick and prmote the most outstanding. Still, i should think that there are at least a few tests a candidate need to pass. Shinra does't need idiots that can't stay calm and think clearly in the face of crisis. Cloud, for example, used to think with his heart before thinking with his brain. He was too emotional. A SOLDIER must be able to handle themselves in any situation and should be able to do their job without hesitation. They should already stand out as skilled or talented individuals. Anyone remember if there were any qualities that the Turks looked for other than brute strength? (Strength was definitely a trait they looked for).
Then there's the issue of mako injections. If the subject lacks a strong will (or, i'd imagine, a strong sense of self and a sense of purpose) then the mako overwhelms their system and results in mako poisoning. In Cloud's case, I'm not sure if Shinra glanced at his application and rejected it, deeming him unsuitable fo the program, or if he actually took some sort of test to see if he would react negatively to the mako. Either way, i think Cloud failed beacause he's a guy whose self-worth is purely dependant on the views of those around him—especially Tifa, who happens to be his reason for attempting to join in the first place. (What would he do with his life if she didn't notice him? If he couldn't be the hero he thought she expected him to be?)
Regarding the will of all the other 1st class SOLDIERs, i think that they had incredibly strong wills. Every one of them had a definitive sense of self (regardless of how they saw or compared themselves to others) and they had a strong sense of purpose (even if that purpose did quickly and drastically change). Sephiroth's will was perhaps the strongest, seeing as he maintained his sense of self and purpose even while being within the lifestream.
Angeal and Genesis were probably given their mako injections because they were better-suited to being weapons. That, and Hollander wanted his Jenova project g to be superior to s, so naturally he'd enhance them with mako and have them join soldier just like Sephiroth. (How else could he proove his experiment superior?)
I get the feeling I've started rambling...