Pre-preparing breakfast scramble -- potatoes
You're right that they will need to cook a bit longer than your other ingredients and you should plan on cooking them separately for that reason.

If you just want them soft then I would dice them and cook them in the microwave until they are done. For the quantities that I prepare it is only 5-8 minutes and they are almost completely cooked.

If you want them crispy then you will need to fry them. Precooking them in the microwave will make the frying go faster and be more even.

After the potatoes are cooked feel free to mix with the other veggies. They will keep in the fridge for a while- the sausage will go off before the potatoes do. If your potatoes were fried you will lose some of the crispiness in storage.

If you need to keep them for more than a week then I would freeze them in individual portions.