My first question as an applicant would be, are you a state certified program?
(TX may be different than OH. In Ohio you don't just "hire" an apprentice.)
Do you offer full tuition compensation for the state required classes?
Those two factors may not seem like good indicators to you, but if a prospective apprentice asked me those questions, I would know his intentions are he wants to learn from a good institution, one that at least meets the state minimum criteria, and that they want to learn.
All of my friends who are machinists are passionate about machining. They enjoy learning new skills, even if just for the sake of doing it. Most work 8, 10, 12, hrs a day machining, and go home and machine for a few more hours. When I was an apprentice 18-20 hour days were regular. If I was working 12's at work, plus 2 or more hrs of class every day, plus a couple hours machining at home.
Finding kids who are passionate, about anything, is a good start. Mechanical aptitude is a plus, if your building tooling, but not necessarily for machining. If you asked my brother if I was mechanically inclined, he would just laugh at you. I have a cousin who is VERY mechanically inclined, he's a mechanic, I won't loan him a hammer for fear of him breaking it. I certainly would not let him use my machinery. I think it is more important to judge their mentality in regards to precision/accuracy.
When my grandfather was hiring, (I know... ancient times) he had two main qualifications before he would consider an applicant. They had to show up in person, first and foremost. If someone called in and asked if we were hiring, he would tell them no. That was his judge of their character. They were too lazy to even show up. Second, he would have them machine a part. He didn't really care if they machined the part correctly, if they read the blueprint right, it was all in how they held the micrometer. How they handled the tools. Reading a blueprint and machining a part can be taught. Rough and crude is a mentality that is not easily overcome.
You have to tailor your aptitude test to the type of work that you do. You will sell yourself short with a complicated math test. Most kids couldn't trig their way out of a wet paper bag. This may be a bigger criteria if you do a lot of manual machining that requires angled setups. CNC... maybe not so much.
Another criteria that you may want to consider, what form of extra curricular activities? Church, Boy Scouts, one of the many community service groups? If you want to hire a long term candidate, it is important to consider more than just their work ethic and abilities. I have a good friend of mine who is a great machinist. I do not think I would ever hire him because of his attitude towards the world and those around him. I have another good friend who is a marginal machinist, who I would hire in a heartbeat, because of his attitude towards the world and those around him.
I think most important, if you are looking for guys to bring up from nothing, is to make sure you make it clear to them, how much you value them and that you have big plans for your candidates.