How can I find out which jobs have bonuses?

Your nearest recruiter will have the most up to date information on which MOS’s are currently offering bonuses for enlistment. That said, I’d advise you to pick a job that you’ll actually have an interest in and enjoy doing because after the money is spent, you’re still under contract to the military for the duration of your enlistment. 5 years is a long time to do something you hate just because someone offered you a few extra bucks.

Neither have a bonus for enlistment.

No matter what job you select, you are a soldier first, however, choosing an occupation you will enjoy learning and becoming proficient in should be at the top of your list of considerations. Twenty years in the military goes fast and when you complete twenty, you are still young enough to start a civilian career. Two pensions makes life a lot easier and happier. Do the math and see how things look? Most federal law enforcement positions have an age limit of 37, must also make allowances for military service due to the training and experience you will acquire over the years. Good luck on your decision. Whoa!