When a plant looks cramped, the natural move is a much bigger pot, so it never needs moving again. It feels kind, and it is the most common way to make a healthy plant sulk. The Royal Horticultural Society (RHS) advises moving up only slightly: a pot about 2.5–5 cm wider than the old one, and not much deeper.
The reason is water. Roots drink from the soil they are touching. Soil with no roots in it still holds water, but nothing is drinking it, so it stays wet for a long time around the roots that are there. Wet soil holds less air, and roots need air as well as water.
Set the width of the pot your plant lives in now, then choose how much wider the new pot is. The picture shows the root ball in its new home and the fresh soil around it. Then pour some water and compare the three kinds of pot.
A pot that is 5 cm wider sounds like a small change, but it is a bigger change than it sounds. If a 12 cm pot becomes a 17 cm pot of the same shape, it holds close to three times the soil, because width, depth and the room around the roots all grow together. Try it in the picture: the soil volume figure climbs faster than the width.
That is why the 2.5–5 cm step is a rule of thumb rather than a limit. A plant with a lot of roots that fill the pot can handle the upper end. A small, slow plant is happier at the lower end, and some plants like being snug. Roots poking out of the holes, or roots circling the outside of the root ball when you slide it out, are the signs it is time to move up.
Water should be able to leave. A pot with a drainage hole does that for you; a pot without one holds every drop you add. Many decorative pots have no hole, and that is fine if you use them as a cover pot: keep the plant in its plastic nursery pot with holes, and slip that inside the nicer pot. To water, lift the inner pot out, let it drain, and put it back.
The unglazed clay of a classic terracotta pot lets some moisture escape through its walls, so soil in it generally dries faster than in plastic or glazed ceramic. That helps a plant that dislikes wet feet and can be a chore for one that likes steady moisture.
Whatever you spend, the same few things matter. First, a width that is a sensible step up: for a plant in a 14 or 15 cm nursery pot, a cover pot about 16–18 cm wide gives it room to be lifted in and out. Second, whether it has a drainage hole, or is meant to be a cover pot; read the listing. Third, the material: plastic is light and cheap, ceramic looks calmer and is heavier. At the lower end a plain plastic pot does the job. In the middle, ceramic gives you weight and a quieter look.
The cheapest pot of all is one you already own. Wash a spare pot, reuse a cover pot from a plant you did not keep, or look for second-hand ones at markets and in free-to-collect groups. A good rinse, and a scrub of any white mineral crust, is all most of them need.