You tea should never become bitter due to your storage methods. The only thing that should happen to tea as a result of how you store it is general loss of flavor or loss of the complexity of flavor (in a green tea, you might lose any honey or fruit notes of a tea that has been improperly stored, but it'll still taste like green tea).
There are a couple of factors at play when storing tea. The first is light. Exposure to light will degrade the quality of tea, stripping it of both color and flavor. Light also sets off a chain of reactions that destroys the antioxidants found in tea. So, you should store your tea in a light-blocking container (like a typical metal tea tin).
The next factor is air. Tea needs to be stored in a place that does not have any strong-smelling other foods or chemicals because it absorbs other odors very easily. In addition, tea absorbs moisture from the air, so it needs to be stored in a dry place. Moisture can cause several different problems with your tea: it could start binding to the tannins and make your tea taste bitter when you eventually brew it, and excess moisture could provide breeding grounds for bacteria or fungus, which would make your tea unfit for brewing at all. So, store your tea in an airtight container that blocks moisture and any other nearby odors. Vacuum sealing is not necessary, unless you want to keep a batch of tea for a long time without using it at all.
I haven't found any evidence supports claims of oxidation affecting taste more than moisture or light. Different types of tea are created by oxidizing tea leaves (white teas are the least oxidized, black teas the most, and greens and oolongs are somewhere in between), so oxidation is not inherently bad for tea.
To sum it up: Protect your tea from the harmful effects of light, moisture, ambient odors, and air by storing it in an airtight container in a cool, dark place. If stored properly, most kinds of tea leaves should retain most of their flavor for about two years, though fresher is always better. (Some teas, like Japanese green teas, are traditionally only stored for about 3 months.)
In order to achieve the best taste, brew tea according to the processor's instructions (at least to start with - once you become more familiar with tea and what you like, you can adjust according to taste). The tea manufacturer's want their tea to taste good, and they are experts, so you can rely on them to provide decent instructions. I've never bought tea that didn't have instructions for brewing right on the package, but in case you find some that don't have instructions, here are some general guidelines. I've taken this from Upton Tea's Brief Guide to Tea, and it corresponds to my own experience with making tea and chatting with tea importers / shop owners, too.
Whole Leaf Teas
- black teas: boiling (212 F) water, steep for 3-4 minutes; if serving with milk or lemon, steep 4-5 minutes
- green teas: slightly less than boiling (180 F), steep 2-3 minutes
- oolong teas: lighter oolongs use warm (180 F) water, steep for 2-3 minutes
- white teas: less than boiling (180 F) water, steep for 2-3 minutes
- herbal tisanes: boiling (212 F) water, steep for 5-8 minutes
Fanning, Crushed Leaves, or Powder
- This is what most pre-bagged teas are, and since they have been processed to be finer, they require a shorter brewing time. (Finer leaves means more surface area, so you get more tannins per second when brewing, compared to tea leaves in larger pieces.)
- Use guidelines above, but brew for 1-1.5 minutes less than whole leaf teas
The bitter taste comes from tannins. There are two ways for tea to become unpleasantly bitter: steeping at too high a temperature, or steeping for too long. (It's also possible that if your water is heavily chlorinated or otherwise impure that it could be making your tea taste bad, but that's far less likely than improper brewing.) If you're making tea from loose tea leaves, using too many leaves could also make your tea bitter; a good rule of thumb is 1 teaspoon of tea per 8 oz of water, though this can vary depending on the type of tea you're making.
Generally speaking, the longer you brew tea, the more tannins will be released and the bitterer the tea will be. If you use the times above as a starting point, you shouldn't get any overly bitter tea, but remember: each batch of tea is unique, and each tea drinker's taste is different. Experiment until you find what you consider to be the perfect cup of tea.
Lastly, start with good quality tea. Some tea is poorly processed and the flavor is ruined before you've even opened the package. If you start with a high-quality tea, you're much more likely to get good results. :)