In the true traditions of the sport, table tennis can be played on any table with a makeshift net and so all you really need to get going are bats (paddles) and a ball.
However, when played properly on a full size table, the game is fast and energetic so you will need some proper clothing and grippy shoes.
Table tennis matches can last a long time and so you will need to keep hydrated.
So always keep your drinks bottle handy when playing or practicing.