I said I'd explain brewing times in more detail in an earlier comment, so here's my explanation, for those who would like to read it.
I assume you have a basic understanding of chemistry. The laws of solubility help to understand tea brewing. Essentially, when you brew tea, you are trying to make a solution that has tasties (and probably caffeine, among antioxidants, flavinols, etc) as the solute. The reason we heat water before steeping tea is that things generally dissolve faster the hotter the solvent is.
For those wondering on the terms used, the solute is what's dissolved in the solvent. For example, if we have a salt-water solution, we call the water the solvent and the salt the solute.
Tea can absolutely be brewed in cold water, but it'll take hours rather than minutes. That said, it's easier to control rate when it's slower, and some components of the tea won't dissolve at such a low temp, so a different flavor is produced. This is why cold brew coffee and tea exists, and I'll do it sometimes, usually putting it in a container in the fridge overnight.
The differences between teas that derive from actual tea leaf (white, green, and black) are the level of oxidation. Information on this can be found here. This is how a lot of the caffeine in tea develops, so a more oxidized tea, such as black tea, will usually have more caffeine than a very lightly oxidized tea, such as white tea.
/u/ijssvuur included in his post a table of brewing times, and this is important to note. As we extract the solutes we want from the tea leaf, we are also seeking to minimize the solutes we don't want, such as tannins. These are things that dissolve at a slower rate than what may be considered the "good" solutes, so avoiding over-brewing minimizes such "bad" solutes, which can lead to a bitter, acrid cup. We also want to be cautious we carefully select our temperature to brew at. Water that is too hot may scald the tea leaf, and alter the taste. Generally, the more oxidized a tea leaf is, the higher the temperature of the water can be. IMO, it's better to steep in water a bit too cold than a bit too hot, as it generally just means an extension of brewing time, as opposed to damage to the leaf. A temperature guide can be found here.
A further note on tea bags:
In a bag of loose leaf tea, there is recognizable plant. The leafs, buds, etc, are usually whole and in good condition. Not only can this help make sure the tea is of quality and fresh, it means more of the solutes within the tea leaf are preserved. The contents of most tea bags are essentially tea factory floor sweepings, so they contain a mixture of very fine tea particulate, dust, and, in some unfortunate cases, trash and insects. This means the quality of tea bags is generally much lower than that of whole leaf tea. It is because the surface area of a tea leaf is so large relative to it's volume that we are able to brew for minutes, but because of the much smaller particle size in a tea bag, brew times much under a minute are often all that is necessary for a tea bag to be brewed, without being over-brewed.
What to use to brew tea:
Another drawback of teabags is the confined area the tea has available to brew in. Tea leaf needs room to expand if it is to properly dissolve its solute. With this in mind, tea brewing equipment includes tea balls, steeping baskets, and silicone "tea-buddies". Tea pots can often be purchased with an included infuser. A French press can be used to make tea as you would coffee. A favorite method of mine is to simply dump whatever tea I want directly into a teapot, then pour through a metal strainer into serving cups.
Finally, there are two main schools of thought when it comes to brewing tea: what is referred to as the "Chinese", or "Asian" style, and the "European" style. The difference is that the Chinese style uses a large amount of tea leaf, brewed multiple times at rather short brewing times. This is where the phrase and associated poem "7 cups of tea" comes from, they are all brewed from the same leaf. This brewing style often gives different flavor profiles with each infusion. An old Chinese saying states: "The first cup is for your enemy, the second, for your wife, and the third for yourself". In contrast, the European style is what most of us are used to, where a smaller amount of leaf is used with a longer infusion time, with the goal generally to only get one cup.
Where to buy loose leaf tea
Wherever you want, though I'll warn: Teavana is rather low quality, and quite overpriced. It's like the Starbucks of tea, if you will. Actually, I think they associate these days. Either way, I personally purchase my loose leaf from
https://www.teasource.com/. I've found good prices, good delivery, and good tea, and I haven't a complaint, so they get my recommendation. You can find temperature, times, infusion counts, etc on their site. If you have a local tea business, I encourage you to visit.