<----- served 20 years regular Army and also worked as a recruiter. I, too, enlisted at 19, soon after dropping out of college.
Couple points. Jobs (MOS) are not assigned/chosen by an individual recruiter, but rather a counselor at the Military Entrance Processing Station (MEPS). Unfortunately, recruiters take blame or credit for success and/or failure after an applicant enlists. Everybody blames the recruiter. U.S. Army Recruiters (USAREC) are merely first-line representatives to the civilian population.
To have a shot at obtaining a "good" MOS, it is absolutely critical that your son scores high on the ASVAB exam. Higher score = more opportunities. Combat Arms MOS (infantry, armor, artillery, air defense, combat engineers) are always short on personnel. Military Intelligence and linguists (Arabic, Chinese, Russian) are other shortage areas. Depending on his ASVAB score, he might be eligible for an enlistment bonus, contingent on MOS.
If your son has earned college credits, have him obtain a sealed copy of his college transcripts prior to his appointment at MEPS. If he has at least 24 semester hours, he can enter as an E-2. 48 semester hours = E-3. This requirement has changed since I enlisted over 37 years ago. Credit hour requirements were much less for advanced enlistment rank back then. I enlisted as an E-2 with 24 semester hours when the minimum was 15.
Physical: MEPS employs medical doctors for the physical screening. If something is wrong, or he thinks something is wrong, tell the recruiter before going to MEPS. Lots of applicants shoot themselves in the foot talking about asthma they had at age 5 or some stupid allergy.
Above all, congratulations and good luck. I had a freaking blast in the Army, and also endured some really tough times. It's what you make it.