Baxters do make great soups, with lots of veg, but your own can be so much better, and there's usually more of it.
I would go with Crumblecookie's ham hock - it does take some time, but like she says, it lasts all week. I often make it on a Sunday to use up any leftover veg.
I don't use so much carrot (carbs) but include leek as well as onion, courgette, cauliflower/brocolli stalks; the celery and ham provides lots of flavour. I usually grate the potato into a separate bit of stock and stir whilst boiling it, to provide some thickening.
You can vary it with diced and skinned roasted peppers for colour, or a pinch of crushed chilli flakes, and for a change from ham, I use the stockpot jelly type stock, usually a couple of chicken ones, or whatever you like. Mmmmm, Perfect.
Then when you've mastered this, you can make your own chicken stock from the carcass/bones