So many plants, so many pots.
For plants that want deep roots you want deep pots. These include: most orchids, aloe vera, african violets, and most of your house plants.
Orchids are usually potted in pots that have holes in the sides to let more air flow through. The roots of orchids need more air than most plants.
If you have a wonderful deep pot and a shallow rooted plant you can fill the bottom of the pot with styrofoam peanuts or some small rocks if you need additional weight. Then put soil in the top half of the pot. Another trick is to take a small clay pot and tip it upside down inside a larger pot. Then fill with soil around and above the pot.
If your plant is top heavy, like rubber trees, or orchids which are potted in moss, weight the bottom of the pot with a few small rocks.
Clay pots don’t hold water as long as plastic pots do. They are also heavy so that large plants are less likely to tip over. You will want a plastic liner underneath a clay pot so you do not get water damage on your furniture. Clay pots are porous. Clay pots should be soaked over night the first time you use one. If you do not soak it over night, keep a close eye on your plant’s water needs for a month, the pot will soak a fair bit of water from the soil for a while.
Plants potted in plastic pots tend to stay damp longer and the pots are much easier to move about. The plastic pots are very cheap and now come in zillions of colors, shapes and sizes.
Sometimes it is easiest to leave the plants in the plastic pots you purchase them in and place that in a cache pot. This is just a flower pot with no holes at the bottom. Then you just lift out the plastic pot for watering.
Woven baskets are nice but rot quickly. It is best to leave your plant in a regular pot. Place that pot inside the basket and use moss to cover the pot.