What is the minimum number and order of routes to take to get the true ending?

You will have to go through at least 13 routes: 10 for the "school part", and 3 in the After Story. While the order doesn't matter for all of them (except for the last three), following a specific order may also help to understand the story itself. Here is a possible recommended order:

1. Misae
2. Tomoyo
3. Yukine
4. Ryou*
5. Kyou
6. Kappei
7. Sunohara
8. Kotomi
9. Fuuko
10. Toshio
11. Nagisa

After doing all these routes, you will be able to play the After Story:

You will have to go through a normal playthrough first. Then you will unlock Akio's route, and after finishing it, you will have the True Ending route.

*Ryou's route is optional, as it won't reward you with an orb of light.

You really need to be careful about Misae and Tomoyo's order, as failing to follow this order will prevent you to unlock an orb of light, and you will have to do these routes again.

Fuuko, Toshio and Nagisa's order is important too storywise, and you will miss some important scenes if you don't follow this order.

For the rest, it's more about the characters' relations. For instance, Kyou's route is the continuation of Ryou's route, so it is better to play their routes in this order.

Now, there is not a perfect answer for what is the best routes order. There are other possible orders which can be interesting, for instance playing Sunohara then directly Toshio's route, as Toshio's story is mentioned in Sunohara's story. So you shouldn't think too much about it, and try to follow your own route order, as long you respect the Fuko, Toshio and Nagisa order and the Misae and Tomoyo's one.

If you want some extra information, like how to enter some routes, this guide can help you in your walkthrough.