To detail the "computer based" careers in the military is too broad a category. There are so many opportunities in the military to be involved in computer based careers you need to reduce the search to what you are interested in.
The military is not about the job you do as much as the opportunities a career can provide. Initially you need to take the ASVAB Test to find out which jobs you may be qualified for. You can take this test while in High School or by meeting with a local recruiter to take the test. The next step would be to take the physical, and if qualified then a job counselor would sit down with you and based on your mental, moral, and physical qualifications you would be able to discuss different career opportunities in different fields.
I served 22 years in the Air Force, retired in 1998, and now am a Senior Principal Engineer/Product Technologist for Dell/EMC Inc. The opportunities I had while in the Air Force helped me to get to where I am today.
Recommend you go to https://www.airforce.com/ and review the career resources there and engage a Recruiter to determine if there are career opportunities you may be qualified for, and interested in.