You don't need a Bitcoin client to buy other people's Bitcoin.
You only need a wallet, in which you can store your coins once you purchased them. For a wallet, you can use a client, but you can also use an online wallet (like the
blockchain.info wallet or [/url=strongcoin.com]StrongCoin[/url]).
Be sure to know what you're doing before storing large amounts of money. If you use an online wallet, you'll have to trust the site and perhaps create a secure backup (export the private keys) in case they go down. If you use a local wallet (client) you'll have to make sure to protect it against theft (by encrypting it) or harddisk crashes (by creating backups, also encrypted of course).