I prefer working with parameters. Since the original UA team had 9 members:
Havok, Rogue, Sunfire and Wolverine for the X-side.
Thor, Wasp, Cap, Wonder Man and Wanda for the Avenger side.
I'll restrict myself to that model.
Avengers:
Photon (Monica Rambeau)
Hercules
Speed (Tommy Shephard)
Ant Man (Scott Lang)
Vision
X-Men:
Monet
Siryn
Prodigy
Manifold
I think the characters selected provide a strong diversity, both in their aesthetic, power sets, and unique perspectives and I tried to limit my choices to folks who don't have active on-panel "home books" currently (that I am aware of)
Many have worked together before. Some are close friends (Monet & Siryn). Some are more than friends (Speed & Prodigy). Some have familial ties (Vision & Speed). Some are simply on each other's radar from past brief encounters (Ant Man & Prodigy). Some have unique ties to the divine (Hercules & Siryn)
They've a wide range of skills and proficiencies beyond their powers that would make for interesting and varying levels of cohesion, cooperation, or even conflict.