Modern gaming platforms are many and varied. Your choice should be based on what you want to do with it and the price you're happy to pay.
Sony's Playstation 3 is the most powerful gaming platform available and also includes a Blu-ray player so you can watch high definition content. However it's network play is limited and it's the most expensive console.
Microsoft's Xbox 360 is almost as powerful as the Playstation 3, provides high definition graphics, but lacks any way to watch Blu-rays. However it's a lot cheaper than Sony's rival console and provides an excellent online gaming experience
Nintendo's Wii is perfect for family fun. There's no high definition output, it can't play the latest and greatest games but it's addictive family fun that everybody can join in with
Sony's PSP ("PlayStation Portable") is the most powerful handheld console, but has a limited amount of games and is much more expensive than Nintendo's DS based rivals. Despite some reports you can't play ordinary Playstation games on the PSP - they have to be designed specifically for the mini-console.
Nintendo's DS / DS Lite / DSi are the most popular handheld consoles, simple to use, cheap and with a multitude of games they're popular for a reason.