What is the right approach to build your resume for a civilian career when accounting for your ADOS time as a Reservist?

OK, the real world of HR managers is that they will give your Resume' about 60 seconds of attention, so focus on a summary of your work experience and education concisely at the first of the resume'. If your military experience is relevant to the job you are applying, lead with those items. If not, keep them for the job experience part of the resume'.
Modern resumes should start with name and address, them that short summary of just how wonderful you are and your major accomplishments that can be read in that 60 seconds, then to work experience and educations. If deployments were the gaps in civilian employment, I would include them in work experience just like a civilian job.
There are a number of good resume' builders on the web, Resume Now comes to mind.
I've essentially been a contract worker for the past decade, so I usually kept a current Resume' and then just updated it. If it's longer than two pages, cut some stuff out. If you don't stand out in the summary, you just don't get called.

most civilian companies don't have any clue about what we did in the military. i have been on a few hiring boards and have asked the other members if they know what a military person is trying to say about their military experience and the answer is always " i don't have clue". the point being, your resume gets you an interview, rarely is someone hired based on a resume alone. you don't need to list every position you ever had unless it is critical for the job you are applying for. for example, on my resume, i have 1 paragraph with 3 bullet points that covers my entire 25 year career. but that will change if the next job i want requires specifics from that time. keep it simple and tailor your resume for every job that you apply for.

Thanks for sharing, much informative.