The short answer
Green tea matches one vessel above all others, and that vessel is a porcelain gaiwan（盖碗）of about 100 ml.
It brews hot, pours fast and lets you drop the temperature as soon as the leaf has given what you want.
A glass pitcher of 250 ml is the second answer, and it is the one to choose for a bud grade.
Glass shows the leaf opening, which with green tea is most of the pleasure.
A thin walled porcelain cup does the same job in a smaller package and holds heat a little better.
What does not match green tea is dense unglazed clay, and the reason is heat rather than flavour.
Clay holds its temperature through a long pour, and green tea is already brewing at 80 to 85 °C.
A few extra degrees of retained heat turn a sweet bud tea grassy, and then bitter.
A small porcelain pot is acceptable if you already own one, and it costs nothing to try.
The match is really about how fast you can get the water off the leaf.
Green tea is brewed in short infusions, and the vessel has to let you end each one the moment you choose.
Anything with a lid you can crack open and a spout that empties in 3 seconds will do.
Why it matters
Heat retention is the first thing the vessel controls, and green tea has the narrowest window of any category.
The difference between 80 and 90 °C is the difference between sweet and stewed, and it arrives within 20 seconds.
A thick walled mug holds its heat and keeps pushing the leaf after the pour should have stopped.
A thin gaiwan loses heat quickly, which is a disadvantage for dark tea and an advantage here.
Neutrality is the second thing, and it matters more than most buyers expect.
Unglazed clay takes up oils and aroma from every session and gives some of it back later.
After a month of one tea that is a feature, and while you are still learning it is a source of confusion.
Surface area is the third thing, since a wide shallow vessel cools faster than a tall narrow one.
A gaiwan is wide and shallow by design, and a tall mug is the opposite shape for a reason.
Cup shape alters the last part, because liquor lands on different parts of the palate depending on the rim.
A wide rim spreads the tea across the tongue, and a narrow one sends it straight to the back.
None of this is ceremony, and all of it is measurable in the cup.
Neutral is safe
When two vessels are close in price, buy the neutral one and keep it for everything.
Porcelain and glass give back nothing, so the cup you taste is the leaf and the water and nothing else.
That is what you want while you are still learning what a green tea is supposed to taste like.
A neutral vessel also lets you compare two teas without worrying about what the pot added.
Run that comparison in a seasoned clay pot and you are partly tasting the pot rather than the tea.
Glazed porcelain is neutral even when it is cheap, and cheap is where you should start.
The glaze is the barrier, and an intact glaze on a plain body works as well as an expensive one.
Check for craze lines and pinholes, because a damaged glaze behaves like unglazed clay.
Glass has no pores at all, so it cannot hold anything between sessions even in principle.
Specialised clay is a refinement, and it only pays off once you know which tea you drink most.
Buy it then, dedicate it to that one tea, and accept that it will never brew anything else honestly.
Until that day, neutral ware is the safe default and the cheaper one.
Building a habit
The vessel that matches green tea best is the one you pick up often enough to know it well.
A session a day in the same gaiwan teaches you more than a shelf of ware used once each.
You learn how fast your vessel loses heat, and you start pouring a few seconds earlier without thinking.
That calibration is worth more than any material, and it takes about a month of regular use.
Buy one size and stick to it, because changing vessels resets everything you have learned.
A 100 ml gaiwan brews 5 grams, and once that ratio is in your hands you can taste a change of a gram.
Consistency also makes bad cups useful, since a mistake in a familiar vessel is easy to diagnose.
Clean the ware the same way each time, and do it without detergent.
Rinse with hot water, wipe dry, and leave the lid off so nothing stays damp overnight.
A pot that smells of anything at all before you start is telling you it was not dried properly.
Replace cheap porcelain freely, because the habit rather than the object is what matters.
The best match is the one you reach for without deciding.