I am a moderator for several poetry mailing lists on Yahoo! Groups. Because of that experience, I usually try to be as helpful as possible when I apply to a group. I try to mention where I heard about the group, and why I am interested in the group.
A terse request for membership usually won't get you rejected for one of the groups I moderate, but it will usually guarantee that your posts and uploads will be moderated in the beginning.
I've found large groups (TastefulTGCaps currently has 881 members) are much more likely to shoot first and ask questions later, than smaller groups. Even small groups can some times have problems if you get a few
trolls or other difficult individuals. :-(