If you want to work in the US after college, you should complete your military service requirements before (preferably) or during college. Right after you graduate, you’re allowed to work in the US on OPT, which comes with your student visa. However, if you leave the US for any length of time after graduation, you lose your OPT eligibility and then you’d need to find an employer who’d petition for a work visa for you - and work visas are really hard to come by.
In addition to the visa paperwork, employers are also much more likely to invite you to an interview if you’re applying locally (e.g. from within the same city) than if they’d have to fly you in from a different country or skype.
Last but not least, if you’re applying for jobs while in college, your college career center would actively help you with your job search. They’d be organizing career fairs, for example, with employers who’re specifically looking to hire students from your university. If you’re applying for jobs later after your military service, you’d be on your own.