Ballard is best known for his novels, but he also wrote a number of exceptional stories — some favourites include "The Drowned Giant", "A Question of Re-Entry", "The Terminal Beach", "The Garden of Time", "Dream Cargo", and some of his earlier stories like "Billennium", "Chronopolis", "The Concentration City" (also published as "Build-Up").
There's a two-volume collection of all his short stories, although it honestly contains more misses than hits. The individual collections "The Terminal Beach" and "Vermillion Sands" are great.
Ballard had several "niches" he operated in. One thread running through much of his work is a preoccupation with physical spaces and architecture, inhabited by alienated characters with some repressed, dark psychological traits (obsessiveness, violence, narcissism) that's held in check by modern society. He keeps going back to the theme of men (they're almost always men) regressing to a "natural" violent state: High Rise, Running Wild, Crash, Super-Cannes, Cocaine Nights, and so on are all about this. His later books are a little tiring because of this; too many books about rich people using violence as a means of psychological release, with a smattering of pop psychology stuff that frankly hasn't aged super well.
Personally, I find his earlier, wilder, more abstract fiction a little bit more interesting the later stuff. I would recommend starting with The Crystal World, which is fantastic.