I'm not the most experienced Anchor user, but here's some pointers that might help you along.
(1) The Hipfire CoF is terrible for any LMG, the LA1 Anchor is no exception to this, so don't expect to get much mileage out of the Advanced Laser Sight. Forward Grip is probably the way to go as you'll want to ADS.
(2) I like to think about engagment ranges as follows.
The LA1 Anchor lives solidly in the CQC regime. Essentially, if you're going to do a biolab fight, bring the Anchor.
Since you expect to be fighting close, use a x1 Reflex sight and Soft Point Ammo. There is also surprisingly little downside to using a Suppressor on this weapon; it only hurts you at longer ranges, which you'll never use this weapon for. As a benefit, this means you can shoot someone without automatically appearing on the minimap, which is very useful in low-pop fights.
Nanoweave + of NMG is recommended for CQC, you may not have the opportunity to duck into cover and regen your shield the way a Resist Shield + ASC build can at medium range. Use Flak + of NMG on higher pop to reduce damage from grenade spam on a capture point. If you're feeling really cocky, you can use Adrenaline shield instead of NMG for streaks and Grenade Bandolier if you're assaulting a high-pop capture. 2-3 frag grenades into a crowded control point can net you a bunch of kills.
As far as CQC LMGs go, the reload is unforgiving at 4/3.37 seconds, so you never just want to spray all your bullets the way an extended max EM6 can. No suppression fire for you and burst your shots! There's really no best value for your burst size. The optimal burst size is one where you can reliably land every bullet, so opt for smaller bursts as you're learning to combat the weapon's kick.
Hope this helps.