I would recommend sampling a few titles that look interesting.
Check out the previews.
Then pick one of those and just go far enough back to where the current writer of that book started. Then go forward from there.
Once you're caught up with that one start looking into your next one using the same method.
Many titles are getting new writers post-Convergence.
DC has a list of the titles along with their writers/artists. You could use that to help decide.
What I would do is what I said above, but if one of the books you're interested in is on the post-Convergence list and the writer hasn't changed, I would definitely start that one now.
The ones with new writers, I would probably wait til June for.
For instance, the books I read:
Batgirl- started with #35 (new writer, continuing post-Convergence)
Grayson- started with #1
Gotham Academy- started with #1
Justice League 3000- started with #1 (getting relaunched post-Convergence but by same creative team)
Mind you, if the current writer of JL3000 started with #10 then I would only go that far back.