You have two situations: Federal and State. I will try to answer both.
Federal Return. You will usually get a better result filing a joint return. This FAQ provides information as to why: https://ttlc.intuit.com/replies/3288477. It is possible, however, that if you have no children, have similar income, and do not anticipate any credits (school credits in particular), separate returns will likely produce a similar result and will be easier to file for the state returns.
State Returns. You don't mention your state of record but, if you file a state return on your military income, you must exclude your wife's income. She is not yet a resident of your state of record. Of course, if your military income is not taxed in your state, you will not have a state return to file. For California, however, your wife will file as a California resident, married filing separately. Here is the California website that explains: https://www.ftb.ca.gov/individuals/Filing-status-information.shtml
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