[quote=@Omega Man]
If your guys are stealthy and/or combat experts and enhanced humans, you'd likely be in the JL Task Force under the leadership of Martian Manhunter, or you would have been involved with the JL International under the leadership of my Capt. Atom as he worked in affiliation with world governments. The JLA is for the more flashy superpowered folk. 
[/quote]

Should I change Jane over to one of the other teams then? I was imagining Task Force since she's British, not American, and Martian Manhunter seems like the best match for her mentor/team leader wise. He's able to see past her exterior more, has a calmer demeanor that she'd appreciate working under and start willingly opening up to, and I could see how her strengths and weaknesses could work for more stealth/infiltration type missions. At the very least, he'd have more patience with figuring out the best ways she could help. 

Zatanna's magic isn't really what Jane does. Batman might appreciate her being more professional than most, but also have to worry about Poison Ivy flashbacks anytime he fights with her. Then she's basically the opposite of Wonder Woman and so the two would clash, though if JL Europe would make the most sense for her, that could make an interesting past dynamic. Maybe she was on JL Europe for a time before getting transferred to the Task Force? Though if JL International would be doing most of the disaster relief type assignments, that seems like it would be her most natural fit.