Will a KitchenAid mixer improve your bread? Maybe. Are they worth having? Absolutely. As far as I can tell, they literally last a lifetime - my grandma has one that was still working when she moved to a retirement home, my mom's mixer is still working after 4 boys who ate anything and everything we could find, and while my wife has only had one for a few years, I'll be incredibly disappointed if we can't pass it on to a kid eventually.
You can also get great attachments for the front for grinding meat & doing other things - they're not just a mixer.
That said, at 4 loafs a week, a decent bread machine is the way to go. Toss stuff in, out comes bread. It's really, really hard to mess up too badly if you follow a small set of recipes you know work. Tip: The yeast will eventually die, so if the bread is insanely dense, get new yeast. If you're going through a lot of bread, this probably isn't a big deal, though.
Also, if your family will eat it, look into potato bread recipes. It's a very heavy bread, and my mom found that all of us were fine with one sandwich made from potato bread, otherwise we'd want two. It's no harder to make than any other bread.
But in terms of "low effort bread," it's really hard to beat a bread machine. They're pure awesome. If you're not sure, get a cheap one at your local pawn shop and see how it works for you, then upgrade if needed. But, seriously, we were going through a loaf of bread a day when I was growing up, and it only takes ~5 minutes to toss a loaf in the bread machine once you've done it a few times. You can also make wonderful dinner breads - I was a huge fan of Sally Lunn bread for dinner. Light, fluffy, wonderfully tasty...
For now I just mix everything by hand or using a handheld electric mixer, and I am weighing the benefits of tossing it all into a standing mixer.
They'll eat more as they get older. A stand mixer is incredibly useful for feeding growing kids cheaply. They're not cheap to buy, but they do pretty much last forever!
I will confess our family spends about $1400 a month on food right now ($200 of which is restaurants, mostly delivery like pizza). Please don't shame me, I know it's bad! I buy almost entirely organic food and naturally raised meat.
O.O *does maths* That's insane. No offense, that's flat out nuts for a family with three small children. My mom fed 4 teenage boys (all of us were runners and swimmers) on a lot less. Lots of bulk purchases from Sam's Club or Costco (depending on which was closer), and a lot of rice/potatoes. A stand mixer is excellent for making mashed potatoes, by the way - cook them, toss them in, mix for a while, and you've got potatoes. Leave the skin in. It's healthy. Or less work. Something.
Seriously, that's more than I'm spending on my mortgage once we move. By about 50%.
My biggest hurdle is really convenience.
I think the biggest costs for my family are snacks and lunches though, not even dinners.
If you don't know, you can't optimize. Keep track of what you spend on food and when it gets eaten for a month or so, and you'll have a LOT more data to work with for cutting your food budget significantly, should you care to do so.
My family can go through 12 wallaby organic yogurts in a matter of days, so even if I buy them on sale at 5 for $4 and get 12 for the Whole Food case quantity discount, it's still easy to plow through foods like this in our house.
So... don't keep Wallaby Organic Yogurt around? Keep carrots, apples, oranges, bananas, etc? And see if you can get your husband to plant a garden if you care that much about the organic stuff.
I think having such a big family is a hurdle regarding making food from scratch. I wouldn't be making one loaf a week, I'd be making 4 or more! Now compound that for homemade yogurt, baked goods, etc. I don't mind cooking but I do not want to be a slave to the oven...
You don't have a big family. Go back about two generations when 6-10 kids was a fairly common number, and that's getting to be a big family. Also, if two of yours are still at home, they're still small. You think they eat now? Wait until they're teenagers... a teenage boy who's active in sports is a good working model of a bottomless pit, and teenage girls aren't much better if they're active. I think I was consuming 4000-5000 calories/day when I was active in swimming & cross country.
I'm hoping to get into the habit of making baked goods instead of buying them, and bread and especially pizza crust. I invested in some good freezer storage containers, hoping that if I can pull things out of the freezer I will be less inclined to order pizza yet again.
What my mom did was cook in bulk. She had some HUGE stock pots (some were large enough that you used multiple burners on the stove to heat them) and would make something like 3-4 gallons of soup, similar quantities of chili, and would freeze it. Butter containers, tupperware, and aluminum foil are great ways to freeze things - spend a Saturday cooking, freeze everything, and you've got "thaw and heat" food for a week or two. As your kids get older, "take a thing of soup out of the freezer, put it in a pot, and heat it" is a reasonable thing to have them do. Rice is easy to make, so thaw a thing of chili, make a pot of rice, heat up some vegetables, and you've got dinner.
You can also get the vacuum sealers/vacuum bags, and freeze things that way. Soup/sauce/chili/etc can be put into a bag. Seal it, freeze it flat (you can stack a bunch), and once they're frozen, if you've picked your bag size right, you can file them in the freezer like books and save a bunch of space.
You may need a separate deep freezer if you're going to go this route, but if you're spending $1400/mo on food, that'll pay for itsself in a hurry - you can get a brand new one for $500-$800, depending on size. I suggest the vertical style, not a chest freezer, since it's too easy to lose stuff in the bottom of a chest freezer and it's hard to get stuff out of it.
Another thing I'd suggest is scheduling your meals out in advance, at least weekly. You eliminate the "Oh, hey, it's 4PM, I should figure out dinner!" stress, and you can shop in bulk for what you need. Once you get a feel for the size of leftovers, you can use them for subsequent nights. Rice one night, goes into a pot pie the next night. Or whatever.
... but, seriously, buy a bread machine and use it. They're amazing.