I made reusable bags out of baby diaper cover fabric and velcro. We can fill these with ice cubes when an ice bag is needed and they don't leak. You could freeze items on a tray or in ice cube trays and fill the flat bags.
Just buy the flat plastic tupperware containers at the supermarket. They'll last forever, and many of them are recycled plastic or can be put in your recycle bin if they get really grungy, depending on what kind of plastic they are. Or re-use them for other purposes, or donate them to a school or shelter or charity store. If you saved any plastic containers from before you decluttered, use those.
I gave up on freezing in glass after three breakages. I'm now using the plastic tupperware stuff I tossed into a box in the garage when I decluttered and I recently bought some more in different sizes. I'm not wrapping food in cloth to freeze it. That's just not going to happen for me. There are times when I'm just not willing to go the homemade route, for safety and health reasons. And convenience. Do what you can and what works for you. Also, give yourself a break. The zero waste police aren't going to knock on your door if you are using plastic for freezer storage or anything else. Cooking in bulk saves energy and money, it's worth having the items on hand you need to freeze foods conveniently and easily. I know I can't live without batch cooking, I can cook on one day and have enough food for two weeks if I have ample freezer containers. Good luck!
Sometimes I use these handmade insulated bags. They are a bit bulkier than plastic zip locks. I still use leftover plastic containers, but wouldn't repurchase. The ss containers at LWP are great quality, bit pricey.
Spacewise, bags do seem to take up less space. Depending on your thoughts about plastic, you could reuse freezer bags especially for fruits, veggies. Liquids you can freeze in ice cube trays (or anything from which you can pop out the frozen product) then store in bags as well…
Also, Beth Terry has just posted a DIY "Better Than Boullion" which could certainly save space. I don't bother freezing broth, rather use primarily the liquid from soaking dried Shitake or Porcini mushrooms that I can get in bulk. I will be making some of the homemade BTB, though.
Which reminds me: dehydrating, fermenting, canning are great alternatives to freezing.
Not sure, but probably: wash and dry the bags well in-between. If you leave in the freezer, not washing in between use, NEVER let your food thaw in it. Some folks have a reasonable aversion to the chemicals in plastic, aside from the fact it lasts forever, and feel that particularly with reuse you're releasing additional chemicals. I personally don't like the idea of reusing flexible plastics, which makes "zip locks" a non-starter. I do like the bags I posted the link to, except that they're opaque and a bit bulkier. There's also other less bulky reusable silicone/plasticky type bags out there (like Rezip), and -of course- you can make your own, as recommended above…
Again, canning is perfect for tomatoes, other acidic food. Dehydrated/dried fruits are tasty.
One last tip, oft repeated: I find it better to freeze your food spread out on a flat surface that you can [once frozen] release it from and transfer to freezer container. That way you don't have a single big block of frozen food and can later remove just the amount you need of the frozen veg/fruit/whatever. I use Silpats that we've had at least 20 years.
FWIW, Biobags are considered safe for food storage, but are obviously too thin to prevent freezer burn by themselves - would not hold up to multiple reuse, work well to containerize gooey compostables.
Thanks for that Beth Terry link on the Better than Bouillon...another purpose for those little jars I have been gathering! It is one of the few processed things I still buy and now I have the option to NOT. Great!
I am in similar situation and have found that having a small fridge has forced changes in my cooking and food shopping habits. We now eat closer to 100% of what is bought and the fridge gets more chances to be cleaned out just by virtue of having so little inside as we approach shopping day. We used to have to compost whole veggies that spoiled before we could get around to using them. We used to clean the fridge only when we had a power outage or moved. Yes, we lived a pretty slovenly existence!
Here are some tips that helped me adjust to using a smaller fridge/freezer and approach zero waste in that appliance:
No more pre-processed items are bought unless absolutely necessary (regardless of whether a freezer or fridge item)
Store what you can outside of the fridge (but some fruits and veggies need to be kept cold so plan your fridge space accordingly)
Actually plan your fridge space so you always have room for what you deem vital, train others to put things back in same general areas
You can plan your space by keeping things in containers. As you use up the contents, wash, dry and replace those containers in the fridge as place holders (this works very well with prepared salad ingredients as they tend to perish if exposed to the dry air in the fridge). Use a vacuum sealer to extend the life of prepped veggies. It may seem silly to put empty containers in your fridge but it will train you to realize the quantity your fridge can actually hold and how much you need to use up before it spoils.
By having a "floor plan" you will be more aware of how much you actually have in fridge and it's condition
Don't buy things just to put them into the freezer to store for "some day"
You pay a lot for that fridge/freezer space, treat it like valuable real estate: keep in it what you truly will use, don't aim to maximize the shelving capacity, try to be able to see everything in there at a glance without having to shift things around.
Eat what you buy as close to the day when you bought it
Get used to either making smaller batches or learn to eat your large batch (say of chili for example) over the course of the week, you can do this by making your excess into lunches for work/school
If you have opened condiments aging away on the door it means you are going for too much variety in your diet. Be honest with yourself about what you are actually going to cook and eat. Can you go elsewhere for your fix? I love samosas and egg rolls but now I only have them when I visit my favorite restaurants rather than buying a large Costco package (usually plastic bags inside of a coated box, neither are zero waste) or stocking up on the ingredients (we want to EAT, not prepare and cook samosas or eggrolls).
I eat a lot of salads and know how to cook. Just because I can buy dressings in glass bottles doesn't mean I have to have 5 types of dressing on the door. I have a cheat sheet of dressing recipes I keep handy and along with one or two condiments from the fridge and some shelf stable ingredients I now quickly whip up my dressing as I prepare my salad veggies. I do not miss the collection of glass bottled dressings. For those rare occasions when I have someone over who wants more variety than my 1 type of dressing, I still have one bottle of store bought dressing on the door. But it is a better view having one bottle versus 5.
if you have.....you can make
ketchup.........French dressing (like Catalina)
mustard.........variety of dressings both sweet and savory
mayo.............any creamy dressing such as Caesar, cole slaw dressing or tartar sauce
So rethink your standard items you are stocking and look for items that are versatile and long lasting.
You may be at the store more frequently following this pattern and that is where you will find your variety (not your fridge/freezer). You might think you are missing out on economizing by doing this, but going to the store more frequently, buying smaller amounts (which bulk produce definitely allows for) may cost you about the same and you will use up closer to 100% of what you purchase. You will see the specially and reduce priced items more frequently. If you cannot manage financially without buying in quantity, try to approach a neighbor/friend/coworker and split up those purchases.
Hope these ideas help get you started!