Depends on which your family prefer, but green beans are nice at the moment, so maybe some green beans and some julienne carrots.
Timings - do you mean for like how long for the chicken (20mins roughly in total), carrots, green beans (10-15 depending on if you like them soft or crunchy) pototoes (depends on how you are cooking them)
The soup will all take about 30 mins as you haven't got a blender, to make sure they are niceeeee and soft
Hope that helps - if not, let me know (or if you need more help)