Due to the different levels of bioactive compounds in tea reported in the literature, the aim of this study was to determine whether commercially available leaf teas could be an important source of phenolics and selected minerals (copper, manganese, iron, zinc, magnesium, calcium, sodium, potassium) and if the differences in the content of these components between various types of tea are significant. It was found that both the amount of these compounds in tea and the antioxidant activity of tea infusions were largely determined by the origin of tea leaves as well as the processing method, which can modify the content of the studied components up to several hundred-fold. The group of green teas was the best source of phenolic compounds (110.73 mg/100 mL) and magnesium (1885 µg/100 mL) and was also characterised by the highest antioxidant activity (59.02%). This type of tea is a great contributor to the daily intake of the studied components. The average consumption of green tea infusions, assumed to be 3–4 cups (1 L) a day, provides the body with health-promoting polyphenol levels significantly exceeding the recommended daily dose. Moreover, drinking one litre of an unfermented tea infusion provides more than three times the recommended daily intake of manganese. Tea infusions can be a fairly adequate, but only a supplementary, source of potassium, zinc, magnesium, and copper in the diet. Moreover, it could be concluded that the antioxidant activity of all the analysed types of tea infusions results not only from the high content of phenolic compounds and manganese but is also related to the presence of magnesium and potassium.