Looking for some advice.

Yeah yo uonl yneed one shielding power if you aer going to use any. I don' tthink you need to use both Barricade and Backlash. I' d say Backlash is probably the better one due to the fact you can move with it  Barricade is best used if you want to camp in one spot for a moment to recharge. It reallly depends on your playstyle and how you plan on playing your Ryder but in general you only need one of the 2 

With that setup, you want to be on the frontline, tanking hits with Tech Armor and Backlash.
Let your squadmates flank and demolish the enemy.

Cora is great for this, her powers are going to synergize really well with yours.
Charge and shotguns will provide a lot of damage.

Vetra is arguably going to overlap with your build, but that doesn't mean it's a bad thing.
Concussive Shot will detonate your Energy Drain if you spec it to prime.

Liam works well with any squad layout, his skillset lets him fit in anywhere.
Overload will always combo with your Energy Drain, and his Frag Grenade is good burst damage.

Jaal will function best depending on what kind of power choices you made; if you picked rifle and weapon upgrades, then have him be your sniper.
If you picked melee and power upgrades, then have him act as a 'ninja'.

Drack will function similar to Cora, i.e. close-range assault. There's something to be said for having both wrecking-balls on your team while you take center.
Incinerate will combo with Energy Drain, you can detonate the same with Throw.

Peebee is Peebee. What that means is dependent on you.
Her Pull will allow you to make Biotic Combos with Throw.

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As for weapons, if you're sticking with Assault Rifles, then you want something mid-range.
You can't go wrong with the classic Avenger, it has no real strengths or weaknesses; the best part about it is that it's available right from the start and it's cheap to craft.
The Beam Emitter augmentation will make your rifle incredibly accurate, and you'll want piercing and stability mods so you're always on target and can punch through cover.

For Armor, I would recommend either the Pathfinder set or the Hyperguardian set.
The Pathfinder set gives you DR, which will stack with Tech Armor, and it's available from the beginning requiring no research from you.
It also gives you more weapon damage, so your rifle will pack more of a punch.
The Hyperguardian gives you more health and shields, which are always useful.

There's nothing saying you can't mix-n-match pieces, say, Pathfinder chestpiece and helmet with Hyperguardian arms and legs.

Which shotgun are you using? Really good ones: Dhan, Scattershot, N7 Piranha, N7 Crusader.. mainly in that order
Spicy Plasma Meatball launcher aka Dhan is really tough one. Scattershot has infinite ammo. Piranha has armor penetration but massive spread. Crusader is quite accurate but needs large magazine.

Dhan without augments is the best shotgun.  With them maybe the Hesh .