A vacuum is not necessary for either quick pickles or lacto-fermented pickles. Pickles made with vinegar are usually in the "quick" or "refrigerator" pickle category. The brine flavors the vegetable. This type of pickle should be kept in the refrigerator and consumed within about a month, especially if you keep your fingers out of the jar (which, introduces a mold risk). Though, the vegetables often get mushy over time, and you may not enjoy that. Because these are "quick", I often only make what I will consume in about a week.
Lacto-fermented pickles are usually prepared at cool room temperature (or cellar temperature, as a wine analogy). Vegetables are placed in a brine (or in the case of cabbage, simply salted and allowed to create its own brine from the leached water). A vacuum is not necessary, but the fermentation takes place in the absence of oxygen, so the product should be submerged. This type of pickle has a longer shelf life given the salt and acidity produced in the fermentation process. They can remain at cellar temperature, though the fermentation will continue. Refrigeration can be used to slow the process and preserve the "sourness" that you like.
Almost any container can be used for either process, though glass is useful because it doesn't retain flavors/odors.