I use a heavy barrel. I dunno, I actually like it quite a bit since I do 95% of my aiming down barrel. The grip I have is for full auto, but when the hell do I full auto, its always burst.
I ran silencer for a while, but god I hated how many extra bullets it took to take someone down and UAVs/Spotting still show you on the map.
Silencers don't effect bullet damage. It reduces bullet velocity down to around ~300 m/s (varies depending on weapon's base velocity), hence increasing drop over range, and increases hip spread by 20%.
If you're going to use HBar, make sure to place it on weapons that need the spread reduction; generally speaking, most AR's and the decent Carbines and non-belt fed LMGs (U100, etc.) don't require one.
Edit: Quick attachment stats can be found here:
http://symthic.com/bf4-attachments?p=list
The benefits of placing one on a weapon have been substantially nerfed relative to BF3; it only affects standing ADS spread, increases muzzle climb by 50% (as opposed to the 10% in BF3), and doesn't affect the damage drop off (e.g. bullets to kill at certain ranges). The benefit is a 50% reduction in starting spread (as opposed to 75% in BF3). E.g. an all-around nerf.
If you're dead-set on creating a burst fire set-up, try an angled grip to reduce the first shot recoil multiplier to create tighter groupings between your initial shots.
I'm still sticking to ergo/vertical grip and a muzzle brake or compensator depending on the characteristics of the weapon, but I've been having a blast with the AEK + angled (to counter the 3.0 FSM) and eventually compensator to counter the wide horizontal recoil pattern of the weapon (MB until then) on the rare rounds I play Operation Fuckfest.
Oh, and for the love of baby jesus, if you're a squad leader and see a commander mark an objective; even if you're not going to it, just mouse over the damn thing and hit Q; you'll get extra points and help fuel your commander's abilities. That and the leadership ribbons this acquires are about as rare as a Mistwalker.