Check state laws on suppressors. Most states only require an ATF Form 4 application. The lead time on this process varies by region, and the ATF’s ability to process the orders. Check your local laws before purchasing.
There are some rumors that you need to have a “Class 3” license to own a suppressor; but, this simply isn’t true. You do have to pay for a “tax stamp” when you first buy the suppressor – but there are no ongoing fees or licenses required. This tax is similar to paying sales tax on a purchase, except that it goes to the federal instead of the state government.