I like several Loki pairings. In my headcannon he dated Sif, Fandral, Darcy and Mobius, he definitely had some cute boys and girls from the palace and the City. I think when they were younger they found it thrilling to seduce some of the guards, just for sex or some short flings. And then of course there was the Daddy Grandmaster who probably made sure she couldn't sit for a while until she reached the top. And I see different dynamics for all of them.
With Sif he'd be more masc. She makes him submit, but sometimes he tries to reverse it. They butt heads a lot and have hot sex after, but the romance is pretty shallow. It's a short but fiery relationship.
Dating Fandral would be easier. He's a goofball around their friends, but an honest and caring partner in private. He takes his time with Loki, and I think he'd be one of the first she'd come out to about her gender fluidity. Of course he's supportive of it. He'd even talk to Thor about the issues she has with him. They break up because they grow apart, but they remain close friends to this day.
Darcy is someone new and exciting, a human, and such a witty one too. She makes them feel younger, and allows them to be their trickster self. They'd play pranks, gossip, and laugh a lot. She'd introduce them to Midgardian things, they'd teach her about the universe. They also grow apart eventually, and while they don't remain as close as Fandral and Loki, they still are soft for each other and will take time to catch up whenever their paths cross.
The guards were just subject to Loki's teenage hormones. He got his nickname Silvertongue around the time, and learnt that he could charm the pants off of almost everyone. So he tried to challenge himself, went for the guards who weren't allowed to give in, and that thrill was half of the fun.
It's similar with the Grandmaster. A means to survive, although Loki enjoyed being treated like the princess she is on Sakaar. But there's no emotion, just sex and pretty clothes, and that doesn't fill the emptiness.
And then there's Mobius. That weird old man who humbled Loki violently when they first met, but who turned out to be so different. He understands Loki, he's mature, he's honest. But he also kept his inner child alive; he's funny, and he cares. He makes Loki laugh, grounds him, offers him a shoulder to lean or cry on. He offers genuine, unconditional love, he listens, and he makes Loki feel like he's worthy. He doesn't just treat him like a prince, but like his prince. He makes the hurtful words of all the others matter no more. He makes Loki genuinely happy for the first time in ages.