I eat a lot out of my freezer. For me, it's a tremendously effectively way of time shifting. I can cook a 22 lb turkey and 5 lb of potatoes, and that freezes to a good set of meals for a single person (easily more than a dozen). Dinners during the work week can then be cooked in under 8 minutes. So while I'm eating out of my freezer, it's rather healthy food, and stuff I really like.
Your biggest enemy is "freezer burn". One thing that will always be happening is that moisture will be moving around in the air in a container. Even tiny temperature fluctuations in a deep freezer will cause ice to sublimate and refreeze elsewhere (closer to the cooling coils - i.e. usually the walls). This, combined with oxidation of the food, is "freezer burn". This reduces food quality, and is the main reason we limit how long we keep frozen food.
A "frost free" freezer goes through temperature cycles, and thus exacerbates the issues with having air in the food container. So the more likely it is that it's in a normal freezer for any period of time, the more the storage medium will matter.
I see you mentioned containers, but a note for folks using bags: Are they freezer bags? If not, they will transmit moisture/oxygen, and thus won't do much to prevent freezer burn. The freezer bags are intentionally made with different forms of plastic that bind together to significantly inhibit the ability of water to move through the bag.
There are a few solutions to reducing the impact of freezer burn, and pretty much any one of these will work:
(1) Avoid having any air (or at least significantly minimize it). This is possible with vacuum sealing. (I happen to be a big fan of my FoodSaver).
(2) Store things like soup or sauces that are already high in water content. Things that are remixed as they are reheated (soups, pasta sauce) are especially fine in this category. Personally, I still try to minimize the amount of air and surface area. This is often best done with some form of mostly - but not completely - filled solid container, like Cranky mentioned (because a ziploc bag and the like will separate from the frozen soup and add significant surface area). If you use glass, it's important to use something designed for it - like dual purpose canning jars since they are tempered glass and are much less likely to crack/break when frozen.
(3) don't store things for a long time.
A few specific examples:
- I pre-cook and store various meats, especially Turkey and Chicken. I freeze both in vacuum sealed "bags" (actually from the roll and I cut it to the required size). Both are frozen under broth, approx 1-2 tsp per 4oz of cooked meat (I generally put in 2tsp, but a bunch of that is sucked out in the sealing process). The Turkey from its own juices, and the Chicken from either a boil of the bones, et al, or from a 50c can of commercial broth that covers a good dozen chicken breasts.
- I vacuum seal portions of fully cooked mashed potatoes (already high liquid content - note I don't add milk or butter before freezing) and partially cooked rice [made with 2/3 of recipe's water and frozen while still undercooked, then add 1Tsp water per 4oz rice - the microwave finishes the cooking job during reheating]
- I vacuum seal pasta sauce as well, but that's because I'm sealing up very small quantities, like 3 Tsp at a time. I want to avoid a freeze-heat-freeze-heat cycle when using small portions. My mom freezes pasta sauce in plastic containers, 2 Cups+ at a time.
- Soups happily go into plastic containers, as they often have enough liquid on the surface to act as a barrier and take the impact of the initial sublimation. Yes, it forms a bit of a freezer-burned surface on the top 1/16" or so, but since it will be mixed back in, the quality is rarely noticed in the reheated product as long as it's not stored for too long.
- Some cookies: I have a cookie scoop and freeze the little balls (put them uncovered on a cookie sheet in the freezer for 30 min) and then put them into a freezer ziploc. Again, the baking post freeze will hide any freezer burn, and mostly these are used within a few weeks at most, so there is very little opportunity to get material freezer burn anyway.
One other note: reheat on 30-50% power. Microwaves have "hot spots" and water absorbs the waves more easily than ice, so the part that melts first will heat up even more. The "off times" allow the heat to distribute and in my experience will improve the quality of the reheated food.
Edit: minor clarification on containers (bags/glass)