What type of chicken soup and vegetable soup?
You don't necessarily need to make a stock for soup, I never bother unless it is a very thin broth of a soup that relies on the sublte flavours of the stock (like Japanese soups).
Here's a simple vegetable soup:
Finely chop an oinon or two and some sticks oof celery.
Grate a potato and lots of carrots, and cube some swede and/or butternut squash/caugettes/pumpkin etc
The combination of veg isn't too important, but don't add too much potato or it could end up too starchy and grainy. Other veg could include peppers, peas, spinach, or more wintery root veg like swede, turnip, sweet potatoes. Once you've got the basic recipe you can adapt the ingredients for your own favourite flavours.
Begin by sauteeing the onion in your soup pot until it is soft and transparant, over a low heat.
Once you're sure the onion is soft and not crunchy, add all the other veg, plus cruched garlic if you like, or a few bay leaves or a bouquet garni, stir all the ingredients so they are covered in a fine layer of the oil (olive oil or butter form the onion sauteeing).
Turn the heat down low, put a lid on the pot and let all the veg 'sweat' for about 20 minutes, stirring regularly, until they are soft and the juices and coming out and it all smells heavenly.
Then, add lots of freshly boiled water to the pot to bring it up to the quantity you want, pop the lid back on and simmer for at least 30 minutes until all the veg are soft.
If you want to use milk or cream, add a little less water to begin with. The milk or cream shouldn't be added till the end.
Instead of water you can use stick if you already have any, or just throw a chicken carcass into it while cooking if you have one to hand (and fish it out at end).
Season to taste, add fresh herbs once cooked if you want, blend it for a smooth soup, leave it for a textures one, or )my favourite) blend half, leave the other half textures. Then if you want it to have chicken in it add flaked up cooked chicken (leftover roast).
Chopped up ham or cooked bacon also nice to add at end.