These words are all used when something is appropriate or perfect for a situation. They are also used when talking about clothing.
When two things match, it means they are equal, or very similar so they appear nice together.
Whereas match usually refers to color and appearance, fit refers to size. If a piece of clothing fits, it means it is the correct size or shape:
We can also use fit in a more metaphorical sense to mean when somebody belongs in a group; their personality or characteristics are compatible with the others:
The verb suit, when talking about clothing, is used more generally for when a certain style looks good on somebody:
More generally, the verb suit means to be appropriate for. We often use the adjective form suitable: