Is it safe to reuse loose tea leaves the next day? What precautions need to be taken for storing tea for reuse

There is an ISO standard for tea preparation.

To quote the summary:

• The pot should be white porcelain or glazed earthenware and have a partly serrated edge. It should have a lid that fits loosely inside the pot.
• If a large pot is used, it should hold a maximum of 310 ml (±8 ml) and must weigh 200 g (±10 g).
• If a small pot is used, it should hold a maximum of 150 ml (±4 ml) and must weigh 118 g (±10 g).
• 2 grams of tea (measured to ±2% accuracy) per 100 ml boiling water is placed into the pot.
• Freshly boiling water is poured into the pot to within 4-6 mm of the brim. Allow 20 seconds for water to cool.
• The water should be similar to the drinking water where the tea will be consumed
• Brewing time is six minutes.
• The brewed tea is then poured into a white porcelain or glazed earthenware bowl.
• If a large bowl is used, it must have a capacity of 380 ml and weigh 200 g (±20 g)
• If a small bowl is used, it must have a capacity of 200 ml and weigh 105 g (±20 g)
• If the test involves milk, then it can be added before or after pouring the infused tea.
• Milk added after the pouring of tea is best tasted when the liquid is between 65 - 80 °C.
• 5 ml of milk for the large bowl, or 2.5 ml for the small bowl, is used.

Every tea can have potentially various grades and different teas will have different qualities. I'm not sure what is available where you are, but if you're fairly new to drinking loose leaf teas, I'd for starters find a store that lets you see, smell and possibly sample various teas. Once you have a better idea of what you're looking for, then online dealers will be easier to navigate.

1. So, firstly, find a reputable store, one where they are knowledgeable about their product, and difference in grades.
2. Ask to smell the teas. Please DO NOT stick your head in the tea, waft it with your hands or the lid of the tin. If you like the aroma, it's a good starting indicator of how you'll like the tea.
3. Look closely, are the tea leaves fairly even in size? An unbroken leaf is generally graded higher than a leaf that is broken/crushed. Though since you're specifically asking about black teas, note that certain black teas are deliberately cut, to encourage a stronger flavour. If the leaves are torn, crushed, it may be a sign of a rough machine harvest, or poor handling. This could result in bitterness. The lower grades (small crumbs and dust) generally end up in tea bags. So, note that.
4. Most importantly, taste it! If the store offers a few different sampler sizes, go for that. Ask the people there, about how they'd recommend you prepare it. And try a few different kinds and grades.

Note, if you're new to loose leaf tea, it should taste different than what you're used to. Trust your taste buds and your nose first... Regardless of what it looks like and the price and what the description says, if you don't like the way it tastes & smells (which is often subjective) the rest is pretty meaningless.