It's quite simple to choose the right containers for your container garden. Simply find out the average root depth of the plant you wish to grow, as well as the average diameter of the plant, then choose a container that is a couple of inches deeper than the average root depth and approximately the same diameter as the plant will be.
If you wish to grow a plant that has an average root depth of 6 inches and grows about 10 inches wide, you would need a container that is about 8-10 inches deep and 10-12 inches in diameter.
The material that you choose doesn't matter so much, although you want to be certain to choose a material that has not been treated with chemicals which might leak into your soil. Look on the bottom of most ceramic pots. If they contain
Plastic is inexpensive, but it typically deteriorates rapidly. It's a good choice if you need to start cheap, but you will probably only be able to use the containers for one to five years before they start cracking and breaking.
Terra cotta is a bit more expensive, but still reasonable. These clay pots are more durable than plastic, but break very easily when dropped, and may also crack and shatter in extreme cold.
Wooden containers work exceptionally well, but can be very expensive. You can buy beautiful wooden boxes for container gardening, but be certain that the wood is not treated with any chemicals. The chemicals could seep into the soil and harm your plants or even make you sick in edible plants. Of course, buying untreated wood means it will rot faster, so that is another consideration. You might buy untreated wood, and then put a sealer on the outside only.
Those are the only materials I've worked with. I don't use much clay, because ceramics break so easily. I use plastic for general purposes, and I use wooden containers for my special plants, my favorites that I grow every year.