Kevin,
There are very, very few real no-no's when making stock, and you've not come near them. The main one is this: there are some ingredients that will dominate a stock no matter what else is used, and these ingredients must either be avoided or used purposefully. Lamb, fish, liver, and greens are the biggies to my palate: they make interesting stocks, but it's hard to imagine what you'd do with a lamb stock except make a lamb sauce or soup, you know? These ingredients, in turn, should only be combined in stock by someone willing to discard the entire result if it doesn't work. Consider: what would a stock including lamb bones, fish frames, and collard greens taste like? An interesting experiment, perhaps, but chances are it'd be horrible, right?
Other absolute no-no's aren't. It depends on what you want. The big one you usually hear about is fat: avoid it. Well, yes, assuming you don't want fat in your stock. But what if you do? There's a Chinese stock, used a lot in certain kinds of Japanese ramen dishes these days, sometimes called "cream stock." Basically you take pork and chicken and scallion and ginger, and lots of pork fat, and you boil it as hard as you can for as long as you can stand it, adding water as need be. The end-result is white from all that emulsified fat, and will never separate. Do you want that? Probably not, but it can be useful.
Don't put in salt. I adhere to this, because I like to manipulate quantities, but some people swear that without adding salt you won't get the fullest extraction of flavor. I think this is an illusion, but whatever. Give it a shot.
Last note. If it's only your family eating, why not use the bones off the table? And the leftover meat scraps. And any leftover sliced tomato and carrot and onion and so on. Use it all. Why not? Restaurants aren't allowed to do this any more, because of certain kinds of pathogens and such, but you know what diseases your family has, so don't waste things. You end up with lots of stock this way, and then you just cook more leftovers in it, add beans and pasta or rice, and serve it forth with grated cheese: healthy, stunningly cheap, and delicious.