I tend to take Mordin or Jacob and Miranda in the early game for bio/tech support since I have the shooting handled. Just got Shock Trooper, with reservations--I appreciate the +100% Paragon/Renegade boost, but the damage boost to weapons and powers is tempting. Also tempted to switch to the Kestrel helmet for stats, since every bit of shield and damage boosting helps and I don't land headshots as much as I'd like for the visor, but I prefer to see Shepard's face during conversations, so it's a tough decision. I will have to set aside some time to agonize over that and the color scheme adequately.
I haven't used AR nearly as much as I should, but I have switched from Flashbang to Geth Shield Boost, which helps now that I'm on Hardcore. I notice everyone and their varren is shielded and targeting me specifically. And I'm burning through ammunition at an alarming rate in each firefight. It's not always that easy wearing down their shields and picking them off one by one while avoiding getting shot to ribbons, but I suppose that's why it's called Hardcore!
There are several ways to improve ammo expenditure rates as a Soldier:
1. Fire in AR as much as possible. It's a straight damage boost, for one. For another, the time dilation can make it easier for less experienced players to track moving targets and repeatedly get headshots. Get into a rhythm with your weapon of choice.
2. Improve aim. (I know, I know.) Fewer missed shots are one thing. Repeatedly nailing headshots with all arms is another. Once you get to the latter, you will start to sail on Hardcore/Insanity.
3. Kill protections with the things best suited to eliminate them. Fire damage or Warp for armored enemies, electrical damage for shielded and synthetic enemies, Warp and Reave for barriered enemies. As a Soldier, this can be accomplished through judicious use of squad offensive cooldowns. It can also be accomplished through judicious use of ammo powers. Set up your ammo powers on your various weapons at the beginning of the mission, and switch between them during combat if necessary. Which ammo powers those are depends on which weapons they are and what kind of play style you intend to use. Synergy should be the key word.
4. If you can, and if it won't get in the way of your headshot spree, use physics damage against enemies after they have been stripped of their protections. They take double damage when ragdolled for whatever reason: Singularity, Pull, Concussive Shot, and so on. Save this for elite and boss type enemies - e.g. Blue Suns Centurions, Blood Pack Warriors, Eclipse Vanguards - so as not to waste cooldowns on mooks easily slaughtered with firearms.
5. Be aware of sneaky tricks with your squad's cooldowns. Using Overload or Energy Drain on a Blood Pack Pyro will detonate the fuel pack for its flamethrower and cause AoE fire damage. Knocking a Husk off its feet instagibs it. With few exceptions, AoE versions of powers are generally more useful than high-damage versions because of how much the AI loves to bunch up.
6. Use your squad's cooldowns on...well...cooldown. The more damage they take off your hands, the less ammo you'll expend. Since AR is the only offensive cooldown the Soldier really needs, you've got plenty of hotbar space to put your squad's other powers. Use it.
Soldier is all about rush, let a squad mate level the ammo powers. Then which squad dudes you take is up to you, but I usually like them to compliment me in some way. If I can strip armor well then I take jacob with fire ammo or mordin with his fire ability iirc.
A Soldier can level AR extremely quickly (especially on a save import file, to say nothing of NG+), at which point she has basically nothing else to dump points into save ammo powers and the passive. Jacob
should get Squad Incendiary but there's simply no reason for the Soldier not to get Inferno Ammo and Squad Disruptor Ammo too.