To get a Class III weapon you first find the one you want and buy it.
Some states will forbid you to own one. Go here to see...
http://www.mp5.net/info/sbsconr.htm
Your dealer will help you fill out the paperwork to send to the ATF to pay your $200 tax. This is what you need to actually take possession. You own it but cannot take it home till the tax is paid.
If you have a corporation...you can skip the CLEO signature and photo requirement. Otherwise... you will need to have the Chief or Sheriff sign off after checking you out.
Send it in with a copy of your prints and wait.
I have a corporation Mine was approved in 15 days.
Price will be high so expect to pay several thousands for it.
Here are the average prices....
http://www.machinegunpriceguide.com/html/subguns.html