Each organization is different in how they house their players. Our son has lived with host families at the Short Season and A levels. I think the Rookie Level players live in the Days Inn in Scottsdale, which is where the rest of the minor league players live during Instructional League and Spring Training.
Host families usually charge $200/month for room and board, but his last one didn't charge anything and even provided a car for him to use. After taxes he's had about $75 to $150 a week to spend on extra food, gas, and entertainment in addition to the $20/day for dinner on road trips. Lunch is provided in the clubhouse before games. He does tip the clubhouse guy pretty generously each week, too ...not sure how much though.
On road trips their teams have traveled in charter buses and usually stayed at moderately priced hotels. At the AA level he will have to rent an apartment with teammates, but I think he's looking forward to that now that he's older.