Start with a little butter and oil in a large saucepan. Dice your prepared vegetables small and add to the oil/butter with some seasoning and a finely chopped onion if you have one. Put on the lid and allow to 'sweat' for about five mins and bring out the flavour of the vegetables. Finally add enough good flavoured stock to cover ... stock cube is fine... and, if you have it, some finely chopped green herbs for extra flavour. Simmer gently until the vegetables are tender. You don't need to puree or mash.
oo, you can make soup with just about anything. You don't even really need a stock cube (personally I find them a bit salty, and I prefer to make my own chicken stock with a real chicken), but of course you can use one if you want. Peel the veg and boil it up until it's tender - potatoes, carrots, parsnips, and anything else you might have to hand. Add coriander to make carrot and coriander soup, add apple (yes really) to make parsnip and apple soup. The potatoes will thicken the soup without detracting from the taste. Or add leeks to the potatoes for leek and potato soup. Once the veg is soft (you're not losing any of the nutrients because you serve it with the cooking liquid), you can mash it up a bit with a potato masher or the back of a fork. It's the cheapest and simplest way of feeding a family - serve with good chunky bread and enjoy.