It's true that keeping air away from most foods will increase their shelf-life, but so-called "vacuum" food containers can't possibly create a powerful enough vacuum to remove all the air. I would be suspicious of glowing reviews with wild claims of their effectiveness.
For the purpose you described, I think you would be much better off using a good quality plastic wrap. Pressed tight against the food all the air is removed and the cling-wrap plastic makes an air-tight seal.
For a fraction the cost of what you're considering, invest in a heavy plastic wrap box that has a sliding cutter.
Because you don't have to struggle with this kind of box, the plastic wrap doesn't get tangled up. You can cut off exactly the amount you need, so it makes sealing up foods very fast and efficient. You can refill such a box with inexpensive store-brand, but it's worth paying a few cents extra to buy professional grade plastic wrap because it stretches and seals much more effectively.
Plastic wrap can be used to seal or augment the seal of most any container you already own, so your choice of size and shape is limited only by the width of the plastic wrap roll.
You can also do things like line a bowl or cup with plastic wrap to hold it while you add the food. Sealing the plastic will form an air-tight, liquid-tight seal that can often stand on its own for refrigerating or freezing.
Although it can sometimes be reused, there's also the big advantage of being able to simply toss the plastic wrap in the trash or recycling bin instead of washing it. Plastic storage containers ("vacuum" or otherwise) are notorious for retaining food odors, and attempting to sanitize them in the dishwasher doesn't always end well.
As Catija points out in the comments, a vacuum sealer is another option to know about.
While it may not be cost effective or practical for everyday leftovers, vacuum sealing in plastic with a machine is beneficial when freezing, marinating, and for sous vide cooking.