Last year I coached two FLL teams(1192 & 1193). I didn't do any screening, and I would not recommend you do that. Between the two teams over 40 students were at the first meeting, and about ten of them were a group of friends, who all seemed to have psychological problems. During the season six of the students were suspended, and one couldn't come to the competition because he was having a expulsion hearing. We did have grade/attendance requirements, so those students were not allowed to return.
After the first two weeks most of the problem students were gone, and I had a good group. I had several of the computer, math, and science teachers recommending students which really help raise awareness of the program.
In previous years we were able to setup a summer school class where we could teach new members how to build/program with LEGO, and get them interested in FLL. In our school district almost anyone could run a class, and what they pay the instructor would more than cover the cost an FLL team.
I'm guessing its a little late to do that now, but its definitely something to look into.
EDIT: Our total cost last year for
TWO teams was approx. $500 registration + field kit, $600 2 Educational NXT kits, $100 snacks for at meetings = $1200 + transportation costs.
If you have any questions PM/E-mail/IM(all in my profile) me.