I've been drinking loose-leaf tea at work for many years now, and have gone through most of these.
- cup with a ceramic or glass strainer.
I've tried both the ceramic type with holes and the glass type with slots. The mesh is never fine enough for me. In addition the holes or slots invariably get packed with leaves and are a pain to clean.
If you mean the tea-ball type, I can't comment. But a steel mesh strainer is my absolute favorite. I've been using the same one (pictured below) for years now and have never noticed any off flavors. Easy to clean: just dump out the leaves and give a good rinse, picking or sponging out the occasional stuck leaf.
Not microwaveable, but you don't want to microwave the leaves, anyway. Microwave the cup with water in it (put a stirrer in to avoid superheating the water. Yes, it can happen, and has happened to me), then put the strainer in when it's the right temperature.
I have never used one, so I can't comment authoritatively, but it seems like at the least they'd be harder to clean.
- fillable disposable tea bags.
I hate disposable anything. I tried the type of bag pictured below and they were a pain. They tend to wick tea out of the cup and onto your table.
As for the other gizmos, I think for tea, simpler is better. The above are the only methods I've used, and I find the mesh basket is far and away the most convenient and best solution.
Water extracts flavor and color compounds from the tea leaves. Water can only hold so much of these compounds before it reaches the saturation point, where it cannot hold any more. Any flavors left in the tea leaves are unable to be extracted by the water.
If you only add 50% of the water required to extract all the flavor and color from the tea you leave much of the flavor behind in the leaves, and the tea will taste strongest of the compounds that are extracted fastest. When you then add the other 50% of the water the tea will be weaker and taste different than tea that has been steeped in 100% of the water needed to extract all the flavor and color.
Best Answer
The differences in quality between teas is usually down to the manufacturer and the product line. As far as I can tell, there is no discernible difference between Twining's English Breakfast tea (for instance) in bags or loose leaf. They are the same leaves, presented differently.
However, and this is the important part, there is a difference in how they infuse. Because of the limitations of the tea bag, and the flow of the water through the leaves, a loose-leaf tea is usually infused more quickly, and possibly better. That is, you get more essence of tea from the leaves into the water. There are different bag designs (pyramid bags for example) which try to bridge some of this gap.
The advantage of the tea bags is that they are easier to work with, as you don't need to strain the leaves out of the water, you can just pick the bag up with your spoon.
There is a lovely essay by George Orwell about making "proper" tea. Some of it is a matter of taste, but his point about the infusion is spot on, in my opinion.