I was about to post in a thread asking which squadmates work best with Vanguard, but off-topic there, more relevant here...
Jack + Sentinel!Shep = <333333333
The gameplay synergy is pretty obvious. Jack can Pull, Shepard can set off combos with Throw and Warp. Also, Jack can provide ammo power for the squad, something that you lack as a Sentinel unless you make that your bonus-power.
On a thematic level it was even more enjoyable. Jack is built like a destructive Vanguard, Shepard OTOH is this literal knight in shining armor. And, in my canon (** HEADCANON ENGAGED!! **), Shepard starts out as an Infiltrator, but Cerberus rebuilds him with eezo to grant biotic abilities (Cerberus is kinda obsessed with biotics). I played to this further with one dialogue-option where Shepard says "I noticed a few upgrades," imagining that was one of the things he referred to. Sentinel was the way to go because it preserves the tech powers, and the biotics (Throw and Warp only) seem pretty basic -- just some forceful application of the mind, nothing fancy. Combat powers? Pfft! Shepard is a good shot, that is all the reflection needed. Pistol/SMG only for the first half is weird, but getting the Kassa Locust really eases that transition. One can see it as a more efficient AR.
In the beginning I do not invest anything into the biotic powers, imagining that his powers are too unstable to use in combat reliably, and then over time I unlock those abilities. Then comes the next fun part of my headcanon: I imagine Jack continually giving him some pointers on how to use his powers (plays nicely to the way her character-arc progresses, I would say).
One of my imagined tidbits of advice Jack gives to Shepard, on casting Warp: "when you see an enemy, imagine two more standing behind him, and aim for the third."
In ME3 I thought of having Shepard's biotics progress even further -- perhaps even supplanting his use of tech -- and switching to Adept or Vanguard, but I found that Sentinel was still more enjoyable an experience for me and stuck with that. I took Energy Drain as a bonus power, and the damage-reduction bonus from that, Tech Armor, and Melee Synergy made CQC really fun. Shepard was pretty much as durable as a (multiplayer) krogan.