Your assumptions are correct. You must first find a class III dealer who has the specific suppressor you want. One example in West Michigan is Silver Bullet Firearms. They require a 50% deposit, and will help you with the paperwork. Another good option is Tigon III Enterprises. He sells them part-time as he is a practicing veterinary surgeon, but he is very helpful.
The paperwork (called ATF Form 4) is relatively straightforward, but does include the need for a passport photo and fingerprints. The most difficult part however is the law enforcement sign-off. You must present the paperwork to the chief of police in your county for his signature. Depending on where you live depends on how easy that will be. Some counties refuse to sign. If that is your case, you'll have no choice but to find an attorney (more money) and obtain what is called an NFA trust. This legal document is accepted by the ATF and eliminates the need for a police signature. There are also several other advantages I'll let you discover should you choose to go down that path.
Yes, this is all very annoying, but it is the price you pay to get that coveted "permission slip" from Uncle Sam.
As for suppressors, I know Surefire is a trusted brand, but they should stick to flashlights. Their Ryder suppressor is made entirely from aluminum. The two things I hate about that is the fact that aluminum will eventually wear out faster than other materials, and aluminum cannot be as easily chemically or physically cleaned without damage. I would strongly recommend you investigate Silencerco's Sparrow suppressor. It is 100% stainless steel, and is the same price as the Surefire. As you have mentioned, this is a lifetime purchase. Choose carefully.
I have acquired two suppressors since they became available. I have a Silencerco Sparrow, and a Thunderbeast Arms 30P-1. I very much enjoy both of them and would encourage you not to let the red tape dissuade you. Suppressors are so much fun. It is hard to describe the enjoyment of shooting without earplugs, especially with your friends and family, and extra especially with new shooters.