This is going to be a long answer, so I apologize in advance and wish you happy reading 
My insurance did not cover top surgery at the time, but this is the process I went through to get my hysterectomy and bottom surgery covered. It's exactly the same, you'll just be asking about a different procedure when you call.
First - Call the benefits number for the plan you'll be on. If you don't currently have a card, you could call HR at the office you'll be working at and ask them to provide it to you along with the group identification number. Call that number and tell them that you are going to be getting on that plan when you move, and want to discuss coverage so that you can make an informed decision about whether or not the plan is right for you. You will need to explain up front that you are transgender. Ask:
- What would be required to have a bilateral mastectomy covered for a transgender person on this plan?
- Can you tell me the names of surgeons who would be considered in network for this procedure under this plan?
- Does the plan include travel benefits if I had to travel to a surgeon?
- What is the out of pocket maximum for in-network and out-of-network procedures/doctors?That will get you the answers to all of your questions. Now, I can try to answer them vaguely here. This should give you a good idea of what you'll actually hear when you call. Insurance can be confusing. My advice would be to read this, call them and take notes or record the call, and then come back here for any clarification you need. Or keep them on the phone longer and get them to clarify.
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For requirements: They will likely need to establish you as a transgender patient prior to approving top surgery. What that means is that you'll need a referral from someone else. It will most likely need to be a therapist, but you could also consider asking whoever prescribes your hormones if you are on them. My advice would be to see what insurance wants and then see what the surgeon wants, and cover all your bases.
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Surgeons and in-network benefits: This is the only unfortunate part of using insurance to pay for surgery. If you want to limit your expenses you will need to go to a surgeon who is considered in network, meaning they already have an agreement with your insurance to accept a specific payment for the procedure. So your choices in who to go to will be limited. You may not even have a choice, there may only be one. Ask for names, and do your research on who is the most appropriate choice for your body type. HOWEVER. You could potentially ask for an exception to have an out-of-network surgeon covered if the results you see aren't applicable to you or the surgeon(s) they have in network don't perform the procedure you need. This will be more difficult if you're only a candidate for DI, as everyone does it.
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Out of network benefits: Let's say you have your heart set on another surgeon who is not considered in-network, but does take insurance (this is key - if they don't take insurance you are out of luck unless you want to pay out of pocket). First, get in touch with the surgeon and make sure they take YOUR insurance. For most plans, you can go out of network and still get some percent of the cost covered, but you will end up with a larger bill than if you had stayed in network. For my plan (I have Carefirst BCBS of Washington, DC), the difference between my in-network out of pocket maximum and out-of-pocket maximum is $2k. So for an extra $2k, I can see any surgeon I want as long as they take my insurance. It is something to think about if you don't think the surgeons they have in network are a good fit for you.
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Travel benefits: Some plans have provisions that will reimburse you for travel and lodging expenses if you need to travel for surgery. Some don't. Some have mileage caps, or other limits on what they'll pay for. It is most likely that any in-network surgeons they have will be somewhere in your state. You'd also want to check if the travel benefits differ for in-network vs. out-of-network procedures.
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Your out-of-pocket expenses are typically inclusive of co-pays and deductibles but you'll want to make sure that is the case. Sometimes it isn't, or sometimes not everyone is on the same page about it. For my plan, this is what all I'm responsible for:

Deductibles are how much you pay in a calendar year for your expenses plus your monthly premiums. After you meet the cost of the deductible, you pay either nothing or you share the remaining costs with your insurance company up to your out of pocket maximum. So if you look at the picture above, I've met my deductible for in-network procedures. If the surgeon doing my bottom surgery is in network, I would need to come up with the last $2170 to meet my in-network out of pocket maximum. For out of network, I'd need to come up with $5344.
My advice is, once you start making firm plans, get things in writing from everyone. If you're budget is very tight, make sure you clarify with providers and insurance in advance how much you are responsible for.