You can do both. If you are qualified, and do not have any deviant mental attitudes which would preclude serving your country, you should probably try to do both.

The Guard (like any military aviation experience) will generally get you head-of-the-line privileges when apply to major airlines. They prefer military trained aviators.

Applying to the guard can take 2 or even three years, so stick with the civilian track until you actually report for military training. If you manage to get hired by a regional before you start the military, that's a bonus because your job is protected while you are away on any kind of military leave and you also accrue airline seniority while you are gone. You could leave as a junior FO and come back and immediately start aptain training.