If you want to "play around" with trading, I'd recommend Bitcoinica.com. BUT the system uses 5:1 leverage, and so you better be very careful because it can wipe out all your deposited money if the Bitcoin price swings in the direction opposite to your bets.
Of course, if Bitcoin swings in the direction you think it will, then you make 5x the profit
Just be careful!
To purchase your first Bitcoins, if you're in the US you should use ExchangeBitcoins.com - they have a bank cash/check deposit feature which is fast and convenient.