Hardened Shields and Heavy Blasters in the front mediums are the essentials for a good Conquest build.
Missiles depend on the rest of the fleet: if you have enough interceptor cover, go with hammer barrages (squalls for AI). If you don't, go with Locusts. It almost doesn't matter what large ballistics you use, as long as you have enough kinetics to reasonably get through shields, because they are all good. Mjolnir + Mk IX is good for 900 range band and is complemented well by autocannons or HVDs. If you aren't afraid to get in close, Storm Needlers are brutal, brutal beasts (I like to put them in the front slots so they get just a bit more range off the forward beam).
Why heavy blasters? Because the Conquest has a massive region forward where it doesn't have good firepower: 2 heavy blasters is a solid cruiser's level of output, which will punish/kill any cheeky frigate or fast destroyer that tries to hang out there. It also allows the Conquest to chase down enemies without stopping offensive output, or do the "swing and blast" maneuver to fire off a dual hammer barrage without the guns stopping.
I do recommend putting the heavy blasters in their own weapon group: if you have an enemy in broadside the ballistics are much more efficient, and sometimes that efficiency is needed. Other times, leave them on and kill the enemy more quickly while running up your own flux.
For hullmods, ITU, Hardened Shields, and IPDAI are solid choices. Resistant flux conduits can be a good choice as well because the shield is narrow. Beware adding too many hullmods: in general they are pricey and should be picked carefully. Personally I prefer LRPD over burst PD, both for the range with ITU and to save OP, but I also tend to put a flak/dual flak on each side for supplemental PD (and the HB's cover the loss of DPS).
Conquest can be run symmetric or not. I prefer symmetric because it lets me engage in whichever direction is most tactically sound, as opposed to needing to circle/move in a particular way. It also lets me have a backup side for when I inevitably overextend during my murdering spree and get one side's guns disabled.