I've been doing container veggies/herbs for the past few years with varying success, although that's mainly because of terrible weather. I haven't tried vining plants yet, so I don't have advice on those. I'm branching out this year, so I'll be watching this thread with interest.
I can tell you that I've never had any luck growing cilantro in a container. It looks great for about two weeks, then something goes wrong. It's a different thing each time, so I can't even pinpoint the source of the problem. As for the green onions, I haven't grown those, but I have grown chives. Mine did much better in a shady spot than in the sun, so maybe try that?
The only other advice I have is to add a little compost to your potting mix and mulch everything. Also, a weak solution of Dr. Bronner's soap will get rid of most garden pests, is non-toxic, and won't affect the plants.