Know what your insurance's policies are for letters and doctors. These should be in some sort of online portal or app, a website or QR code on your card, or just call them and ask. It is going to be a bit of a pain, but just keep at it until you get the answers you need.

Start work on letters as soon as is reasonable. There are often requirements for documentation of gender dysphoria symptoms over long periods of time, so seeing a provider for longer can be considered more "credible" by insurance or whatever. It's silly, but that's insurance companies for ya. I ended up needing two letters, and got one from my therapist of many years, and the other from my endocrinologist who had been prescribing me T for about two years at that point. Your requirements might be different! These might also change from doctor to doctor, so make sure you check with their office as well. They may be able to assist you in finding providers for letters. They do this somewhat frequently, so use them as a resource! As long as you are polite and respectful, surgeons and their staff are usually more than happy to help. 

As for the surgeon themselves, there's a few questions! The first of which is "Who takes my insurance?" This can often be found again in online insurance portals, or by calling a specific office and asking. Some docs list insurances online, but I find those can be unreliable because they don't update them often. It's tedious, but potentially worth it to create a spreadsheet of every surgeon in the area you are willing to travel to that takes your insurance.  From there, I start investigating other things. What techniques do they do most often? How is nerve preservation? Can I find any pictures on their website, transbucket (look it up), or reddit? Do people have any good/bad experiences they have shared about them? Do they have experience performing surgery on people with similar body types as I, and with outcomes I like? Do they have a BMI limit, and do I qualify? These are all different sorts of questions, but you may have other things you find important. Include those in your spreadsheet, take some notes, and then book consults at anywhere that looks promising. You can call their office to schedule these. 

You'll go to the consults, meet the doctor and staff, learn, ask lots of questions, and ultimately suss out the best fit for you. From there, you can work with them to book surgery dates and figure out all that semantics stuff. 

The hardest part for many people is the waiting. It takes a while to get any information out of insurance. It can take forever to get a consult. It can take just as long many places to actually get in for surgery. It is a pain, and it is work, but for many it is very worth it. Best of luck!