A lot of this is dependent on class. As a Vanguard for example, you'll probably never want to use an Assault Rifle - they're just too heavy, and as a Soldier, you'll usually give SMG's a pass - everything they can do an AR does better. Meanwhile, an Infiltrator gets lots of bonuses when using their trusty Sniper Rifle, evening if irresponsibly shooting it from the hip.
The second consideration is range: at very long ranges, a Sniper Rifle offers top notch accuracy. AR's and Pistols Can be pretty good. SMG's can be flaky though, and shotguns are nigh useless. By contrast, Shotgubs ate devastating at short range, but the loss of peripheral vision while looking down that sniper scope can get you killed.
The next consideration is the defenses of your opponents. Slow firing, high caliber weapons like Sniper Rifles and Pistols chew through Armor, but are weak against Biotic Barriers and Shields. Rapid fire weapons with a lot of projectiles, by contrast, like SMG's and Shotguns chew up Shields and Barriers quickly, but have trouble with armor. Assault Rufles are a bit of an odd duck as they're 'pretty good' at handling everything.
Additionally there are mods availiable for several weapon types that alter their capabilities. You can add Armor-penetration to an SMG or a shotgun, or a melee upgrade to a pistol or shotgun. Maybe a scope on your SMG to improve its mid-long range performance?
Finally, you may want to pair some weapons up with certain specialty ammo. For instance, SMG's are devestating in combination with Cryo or Incendiary Ammo as their high rate of fire gives them more opportunities to proc the special effects provided by these ammo types than, say, a slow firing shotgun.
I found this list of biotic and tech combos on the Bioware forums.
Biotic Combos
Singularity --> Warp, Throw, Shockwave, Charge, Nova, Cluster Grenade, Reave
Stasis --> Warp, Throw, Shockwave, Charge, Nova, Cluster Grenade, Reave
Pull --> Warp, Throw, Shockwave, Charge, Nova, Cluster Grenade, Reave
Warp --> Throw, Shockwave, Charge, Nova, Cluster Grenade, Reave
Lift Grenade --> Warp, Throw, Shockwave, Charge, Nova, Cluster Grenade, Reave
Shockwave (only with Rank 6 Lifting Shockwave evolution) --> Warp, Throw, Charge, Nova, Cluster Grenade, Reave
Reave --> Warp, Throw, Shockwave, Charge, Nova, Cluster Grenade
Tech Combos
FIRE EXPLOSION
- Can be set up by: Incinerate, Carnage, Inferno Grenade, Incendiary Ammo
Can be detonated with any Biotic/Tech/Combat powers that can deal direct damage (except for the powers that are used to set up the combo).
Effect: Enemies effected by any of the fire based powers, cause an AoE fire explosion, once they are killed by a direct damage power. The effect is similar to blowing up Pyros with Overload in ME2.
Note: Enemy MUST be killed by the second power, in order to cause a Fire Explosion. E.G. it will not work, if an enemy is hit by Incinerate --> Overload, and still has HP left after that. So, in this case, Overload would have to do sufficient damage to outright kill a burning enemy, in order to cause a Fire Explosion.
CRYO EXPLOSION
- Can be set up by: Cryo Blast, Cryo Ammo
Can be detonated with any Biotic/Tech/Combat powers that can deal direct damage.
Effect: Frozen enemies killed by damage based powers, cause an AoE cryo explosion, freezing any enemy that is nearby.
Note: Same as Fire Explosion, frozen enemies MUST be killed by the second power in order to trigger Cryo Explosion.
TECH BURST
- Can be set up by: Overload, Energy Drain, Disruptor Ammo, Sabotage
Can be detonated by any Biotic/Tech/Combat powers that can deal direct damage (except for the powers that are used to set up the combo).
Effect: Enemies effected by electricity based powers, discharge multiple electricity bolts to nearby enemies, when hit with direct damage powers. Effect is similar to Overload's Chain Overload upgrade.
Note: Unlike Fire & Cryo Explosion combos, this one doesn't require an enemy to be killed by the second power. E.G. enemy hit by Overload --> Incinerate will produce Tech Burst, whether he is killed by Incinerate or not.
Best Answer
So far, with my vanguard, the best loadout I can carry is this combination:
This combination keeps my recharge speed maxed at 200%. This is with the +35 weight capacity upgrade taken at Rank 5 Assault Mastery.
If I swap out the Predator for a M-77 Paladin V then my recharge speed drops to 196%
I might be able to improve this in a New Game+ by upgrading the weapons even further, but on my current run this seems to be the best I can do.
Combination #2 if you prefer sniper rifles:
I'll keep you updated if I find lighter weapons.