Suatg -
Good topic. Just for background. I have no kids. But I spent 4 years teaching and the last 5 years working with high school baseball players and their families during the recruiting process.
Your first question about "important qualities in a tutor" is a good place to start. Obviously you want to pair your son with someone that has the subject knowledge. The more knowledge the better (perhaps). But just like in finding a hitting coach, the relationship between teacher and student may be as important as anything. If after the first few sessions your son doesn't seem to be meshing well, don't be afraid to try someone else. Just because a coach doesn't mesh with a player doesn't make that player or coach bad, just means they don't mesh. Hitting & test taking is all about confidence. Find the person that works well with your son.
Couple of notes...
The teachers in his high school probably offer tutoring sessions during free periods, before or after school. I'd recommend going to his teachers sessions. That effort alone can push the grade from B+ to A. But to go back to relationships, he may want to sit in on other teachers sessions to see if the way that teacher communicates the subject matter clicks better with him. And most of these sessions are probably free.
There are "professional tutoring" sessions. Do your research. Ask some other parents. Ask those companies to provide some references. Just like anything else there are good companies and not so good ones.
Keep this in mind...I may offend some people here... this is a BASEBALL board. The likelihood of earning any substantial scholarship (read full ride) is slim. The math just doesn't work. A student is much more likely earning scholarship money through strong academics then through baseball ability. So if you were looking to "invest" in the future, academics would be the smart bet.
I often tell parents the following...
1 - Want your kid to get a "college" scholarship? Get him a tutor. (They usually get excited then disappointed.)
2 - Want your kid to get an "athletic" scholarship? Tell him to quit playing baseball and go play football. (Its simple math guys. 85 vs 11.7)
3 - Want your kid to play college baseball? Totally doable! Just don't expect the coach to pay your entire bill. (Parents of younger parents begin to regret the 10's of thousands they spent on lessons only to make their kid "this" much better.)
You son has not gotten to SAT time yet. But here is a parting story. Family I know was ready to send their son to a nice private D3 school. Right place for the kid. Many privates have high retail costs. Here's a secret, nobody is paying retail. First place to look is on their "Tuition & Fees" page on their website. Usually you'll find a spreadsheet that tells you if your kid has X GPA & Y SAT he qualifies for the "Presidents Scholarship". The higher the numbers, the better the scholarship. This particular family invested $1,000 prior to senior year on an SAT prep. Keep in mind the kid was already above the minimum's to get in. After the prep class his scores went up enough to move them to the next level of scholarships. Saved the family an additional $5,000..... per year! Good luck getting that kind of ROI with a pitching lesson.
Good luck.
Rich
www.PlayInSchool.com
www.twitter.com/PlayInSchool