Transport belt settings: Read contents, hold signal.
Inserter settings: Chest inserter has a stack size of 1, turret inserter has a stack size of 2.
When the system is at rest, the gun turret is full of ammo and the belt has three magazines on it (four if you point the belt at the chest). When the gun turret needs more ammo, the turret inserter takes two magazines and the chest inserter replaces one. The chest inserter cannot replace all three magazines before the turret inserter takes at least one of them, and so there remain fewer than three magazines on the belt while the gun turret is requesting ammo.
Burner inserters are used here mostly for a clean visual, though they do have a real use. Their slow speed means fewer magazines going into the gun turret, which means less ammo wasted on sounding the alarm*.
Oh, and if you do choose to build this little proof of concept, test it at night. During the day, the lamp will flash 'no power' even when the power switch is closed.
As you might be able to tell from the displayed stats, if you can make them out, I do not have enough problems with biters to warrant a whole bunch of lasers. Placement of the spotter turret is untried -- too far out and it might get chewed on, too far in and the lasers lose their range advantage. (I've been able to protect my gun turrets from damage by putting some yellow belt right at the edge of their range. Spitters can't get into range and biters get hung up on the belt, and they can all be killed before they start attacking the obstructing belt. Then again, the only attacks I get are expansion attempts, and they're about a dozen bugs apiece. No behemoths yet.)
*You don't need any ammo at all with an accumulator-based switch, but those are a little... intimidating? This is one circuit wire.