Traditionally, for home curries, the 3 common veggies are onions, potatoes and carrots. You cut the onions in big 1-mouthful chunks (not finely diced - you want to be able to see them and eat them as a vegetable in the final dish), cube the potatoes to a biggish two-mouthful size, and cut the carrots into rough triangles - you do this by cutting the carrot as if you were thickly slicing it, but turning the carrot a quarter-turn before making each cut, resulting in even, chunky triangular bits. Video demo of ran-giri here:)
The cooking time should be timed carefully after you put in the potatoes (last, just before adding liquid) as they can quickly dissolve into nothing if cooked too long. Remember to serve with short/medium grained rice.
TIP: to make a richer tasting curry, add a small cube or two of dark chocolate after putting the roux in.
OTHER HOME VARIATIONS: My personal preference is to use onion and a variety of mushrooms. To make a milder, gentler curry for children, parents add a couple of tablespoons of honey, and a finely grated apple or two. 'Katsu-kare-' is placing a crunchy sliced hot schnitzel (like chicken or pork) on top of each serving of curry before serving...it's delicious, but this is a lot more work. Often curry is served with 'fukujin-zuke' red sweet veggie pickles on the side. There are loads of interesting variations that people come up with, so it's fun to just experiment with what you have, too.
It's an easy, no-fuss family dish...the equivalent of macaroni cheese, so using boxed roux isn't cheating; it's normal :)
You can make lots and eat it again the next day or two, as curry rice again, or on udon noodle soup (kare- udon). We often came home after school and ate it with toast for afternoon tea lol. You can't freeze it though, as the potatoes go very weird.