Types of containers and their pros and cons
What container you use can have a great difference in how your plant will act. Some plants will prefer one container over the other.
Gardening in containers can also be a great option for those still learning how to garden as you can move them around and experiment more easily.
Also, one important thing to keep in mind is leeching. Whilst this rarely affects inedible plants (often decorative/flowers), it might be something you will want to keep in mind when growing edible plants. Certain pots aren't made for growing food in, and can contain harmful chemicals that can slowly leech into your plants.
Pros: heat up quickly, cheap option, readily available, do well in shaded positions, lightweight, good drainage, easy to drill more holes
Cons: can overheat, little insulation, sun damaged easily

Pros: visually appealing, come in many sizes, easy to drill more (drainage) holes, relatively cheap
Cons: little insulation, possible leeching, can be sun damaged

Pros: last long, visually appealing, can help retain heat
Cons: prone to cracking if frozen, lightweight pots chip easily, breakable, hard to repot from, can stain, can be too porous, concrete can leech lime (toxic to some plants)

Pros: good insulator, lasts very long, environmentally friendly, even faux stone planters can look 'real', visually appealing
Cons: breakable, heavy

Pros: visually appealing, DiY-able, durable, doesn't break easily, may require maintenance
Cons: some wood treatment can be toxic and leech, eventually degrades/rots, can attract pets

Pros: attractive, durable, age well
Cons: can rust (especially in warm, humid areas), can leech toxins, non-porous (bad/no drainage), can be heavy

Pros: good insulation, cheap, lightweight, easy to clean
Cons: unattractive, can leech when degrading or damaged

Pros: self-watering, good for plants that like 'wet feet', reduces frequency of watering
Cons: can cause waterlogging, usually unsuitable for larger plants/trees

Pros: inexpensive, allows for vertical designs, available in a wide variety, available in self-watering designs
Cons: heat and dry quickly, can drip water on everything below

Pros: cheap, can be made UV resistant, very compact when empty, good drainage, great variety
Cons: can break, can lean, generally seen as a temporary container

Pros: attractive, can weigh down light pots to avoid them falling over, easy to 'repot'
Cons: only for decorative value
Do you have more knowledge on this? Kindly send your information to @Mandy Onderwater . Corrections, additions and questions are always welcome!
Gardening in containers can also be a great option for those still learning how to garden as you can move them around and experiment more easily.
Also, one important thing to keep in mind is leeching. Whilst this rarely affects inedible plants (often decorative/flowers), it might be something you will want to keep in mind when growing edible plants. Certain pots aren't made for growing food in, and can contain harmful chemicals that can slowly leech into your plants.
Black plastic (nursery)
Black pots, most commonly used in nurseries, are a great versatile pot. They are light weight and easy to use. They also come in a large variety of sizes, to suit your plant's needs. They usually also come with more drainage holes than, for example, terracotta pots. This helps them drain more easily.Pros: heat up quickly, cheap option, readily available, do well in shaded positions, lightweight, good drainage, easy to drill more holes
Cons: can overheat, little insulation, sun damaged easily

Coloured plastic
Coloured pots are a great addition to your garden. They can make the area look more lively with their colours, and you can mix and match your plants with them. They can be more appealing to the eye than their black counterparts, and might be more "fun" if you want to teach children how to garden. Lighter coloured pots also tend to heat up less quickly than darker colours.Pros: visually appealing, come in many sizes, easy to drill more (drainage) holes, relatively cheap
Cons: little insulation, possible leeching, can be sun damaged

Terracotta, ceramic and cement
These are often the more visually appealing pots. They usually have a higher durability than their plastic counterparts, as sun damage isn't as much of a thing anymore. They are often porous which 'can' assist with evaporating water on all sides. Sadly they often come with only one drainage hole, and drilling more holes can be rather tough if you don't want to damage the pot. They do come in more colours than their stone counterpart. Clay (and ceramic) pots have been used for thousands of years, trusted and true.Pros: last long, visually appealing, can help retain heat
Cons: prone to cracking if frozen, lightweight pots chip easily, breakable, hard to repot from, can stain, can be too porous, concrete can leech lime (toxic to some plants)

Stone
Stone is a very sturdy and often appealing container. They can have loads of character, you won't lieky find in any other pot. They last very long and usually age well, only adding to it's character. They are, however, more expensive and very heavy. They do have cheaper faux stone options, which are lighter.Pros: good insulator, lasts very long, environmentally friendly, even faux stone planters can look 'real', visually appealing
Cons: breakable, heavy

Wood
Wooden containers can have loads of character and can be very attractive. They are easy to DiY and are relatively cheap. Downsides might include that they require upkeep and will slowly degrade over time. If treated right they can last for many years to come. They can be heavy, especially if wet.Pros: visually appealing, DiY-able, durable, doesn't break easily, may require maintenance
Cons: some wood treatment can be toxic and leech, eventually degrades/rots, can attract pets

Metal
Metal can be made in many ways, shapes and forms. They can have very attractive looks, and some get prettier as they age. These pots are most commonlu used as decorative planters. They are very ruable and don't chip, crack or break. They might dent though.Pros: attractive, durable, age well
Cons: can rust (especially in warm, humid areas), can leech toxins, non-porous (bad/no drainage), can be heavy

Polystyrene
Polystyrene is a lesser common pot, as it doesn't usually last very long in warmer climates. It can also be fragile as it can slowly crumble away when you touch it.Pros: good insulation, cheap, lightweight, easy to clean
Cons: unattractive, can leech when degrading or damaged

Self-watering
These pots often have a reservoir at the base of the pot and can be handy in hard to reach locations, like hanging pots. They can also help retain water for longer in places that tend to dry out quickly.Pros: self-watering, good for plants that like 'wet feet', reduces frequency of watering
Cons: can cause waterlogging, usually unsuitable for larger plants/trees

Hanging and wall mounted
These options allow you to make the most of your vertical space and can have a decorative touch.Pros: inexpensive, allows for vertical designs, available in a wide variety, available in self-watering designs
Cons: heat and dry quickly, can drip water on everything below

Grow bags
Grow bags come in many shapes and forms, some even with additional functions like a flap to pick rootstock from the bottom. They are lightweight and relatively cheap, especially for the sizes they come in. They also can come in upside-down grow bags, which has it's own pros and cons.Pros: cheap, can be made UV resistant, very compact when empty, good drainage, great variety
Cons: can break, can lean, generally seen as a temporary container

Bonus: Cachepots/double pots
Cache pots are a decorative outer pot, that you place (usually a plastic) pot inside of. They are decorative ornamentals, that can hide unattractive and ordinary pots.Pros: attractive, can weigh down light pots to avoid them falling over, easy to 'repot'
Cons: only for decorative value
Do you have more knowledge on this? Kindly send your information to @Mandy Onderwater . Corrections, additions and questions are always welcome!