1) What are useful doctrines for this list?
Doctrines add flavor, take the ones you like the look of because most aren't overly effective for their cost but you don't need to take any at all. Iron Discipline is always handy, so are the free ones like Drop Troops and Close Order Drill, the rest are pretty well up to personal preference on weather you pay for them or not.
2) Is a vox-system even necessary in this list?
The Vox is a liability at this level, you almost have a squad per HQ so you should find it easy to keep everyone in the leadership radius.
3) Does every squad really need to buy a vox to make it work, or have I misread something?
Only the Squads that you want to use the Vox network need a vox, this usually means all of them however they aren't mandatory.
4) How can I make this list better, given what is in the Boxed sets?
Lascannons, or at least Missile Launchers. Autocannons just won't cut it when your opponent decides to field two heavy Tanks as well. The Battle Cannons on the Tanks have about the effectiveness of a Lascannon, however they usually have much better targets than vehicles.
HQ
Command Squad
- HSO w/bolt pistol, power weapon, carapace, refractor field, trademark item
- Commissar w/bolt pistol, power weapon, carapace, refractor field
- 4 Guardsmen, 1 master vox & 2 grenade launchers
I highly advise you to trop the Vox. At this point level you can't afford to spend the amount required to make it good and still keep the rest of your army compeditive. Lose the Commissar, downgrade the Officer to a Junior and lose pretty much all the wargear. A Veteran with a Company Standard is a quite nice edition and will keep your men on the field.
While you do have a Vox here, I'll give you a little advice. First off the Trademark Item doesn't work down the network and is not much cheaper than the standard, where as the standard will at least effect the Squads close to the Command HQ as well as the HQ itself. Secondly, don't tool up a Master Vox HQ. You want this squad hiding behind a hill or off the board while being as cheap as possible. It is very expensive and already screams shoot me in neon lights, sticking wargear on a Vox HQ will tempt you to use it for reasons other than the vox and pretty much flush even more points down the toilet when the opponent spies it.
The LD10 Vox you have running here is the minimum you want in a Vox HQ since you can get LD9 troops much cheaper. Do drop the vox though, to many points spent on it.
TROOPS
Infantry Platoon X2
Command Section
- JO w/bolter
- Vox-caster
- Heavy bolter & grenade launcher
1st Squad
- Vox caster
- Autocannon & grenade launcher
2nd Squad
- Vox caster
- Autocannon & grenade launcher
With the doodads cut from the HQ, you should be able to affort 2 more Squads. I suggest Missile Launchers to actually give this list some anti-tank weaponry, not everyone is going to take a Slugga Boy swarm for you to shoot at. The AP3 on the missiles will also drastically help against Marines and other hardened foes.
HEAVY SUPPORT
Leman Russ Tank X2
- Heavy Bolters & pintle heavy stubber
I am going to assume this has the Heavy Bolter Sponsons as well.