I disagree about the avoiding Bushmaster. In the last twenty odd years I have fired well over 100,000 rounds of mixed density ammo through three separate Bushmasters with no problems.
My current AR is a Bushmaster modeled after the Colt XM-15A1, commonly known as the Commando. Cost me $800 delivered to my door and has fired well in excess of 10,000 rounds of varying grades of ammo with no issues.
Regarding the suppressor a "permit" is not the correct terminology - what you will require to lawfully possess a suppressor is a one time tax stamp acquired through either the BATFE or a licensed class III dealer. The stamp is for just the suppressor which may be switched between weapons of similar projectile diameter.
Remember though, firing ammo which exceeds the sound barrier will still result in a muzzle signature although depending upon the pressure the fired ammo operates at - the muzzle signature may be attenuated somewhat.
The real benefit to a suppressor is heavier projectiles at lower velocities which may require some tuning to get an AR styled weapon platform to operate reliably.
If you are set upon acquiring a suppressor your AR barrel will have to have a slower twist or rifling rate to stabilize the heavier projectile in order to achieve repeated accuracy with subsequent shots.
Nice Try = You Suck Spelled Differently