My suggestion is to choose the school which fits his academic abilities, as well as, what school will provide the best avenue for his athletic development. It may be the school which has the best coaches that will help him develop his skills (I hear he is AA ability but everyone can learn) and provide the best competition available to challenge him to even get better and the visibility of playing against/with the best and succeeding.
Choosing the most expensive school if that fits will not matter if he can come out with it being a better athlete and possibly a better signing bonus, but you have to weigh the risk of having to pay the balance, although if he is that good, why not ask for more money.
On the other hand, if he does select a certain school, if drafted out of high school, most team will commit to pay for his college with specific conditions, so having a higher priced school could be an advantage in the over all compensation during the draft, but it also may play against you in a team may not want to pay the additional cost of a high priced school.
Some schools tend not to loose their signees; Stanford for example tends not to loose their signees due to the fact that it would take a lot to sign the player, even above the tuition cost.
If you think your son wants to go pro out of high school, you really need to make sure the teams understand your signability as it can hurt you if you go to a strong school and do not communicate your true intentions to the teams.
BTW one of the top pitchers, 1st round draft pick, out of the sunshine state that pitched 100 mph in HS is in MiLB A after two years…