He may want to get a computer once he gets there, but won't need it before that. I think the security clearance process could start at any time, and they'll ask for various references and other information. I imagine you're right that it will probably be pretty straightforward for your son.
I'll send you a message with more info.
It's been a couple of years so things might have changed but my son started the security clearance process during his second or third week of boot camp. He waited in Florida to "class up" for about a month while the clearance was processed. They are given priority with the department that processes clearances.
They can not use their own computers for classes due to security reasons. We took our son his computer (and phone) when we went to his graduation from boot camp.
The clearance can be finalized long before your son will be placed in a class. That is not the only determining factor. Instructor availability, class size, number of recruits waiting to class up all come into play. While they are waiting for their class to start, they are assigned jobs on the base. There is no way for you or your son to know ahead of time when he will start, or when he will finish.
The classroom computers are special machines. They stay in the classroom and no personal electronic devices are allowed in the classroom. He may have his personal devices in his living quarters.
I understand if you feel frustrated. I'm a planner, but the Navy doesn't care about that, lol. Welcome to the roller coaster!
I forgot to mention - you are more likely to get timely responses by posting in the comments section. Discussions and their replies do not always come through to email.