For that budget, and for a second (non-gaming) machine, I'd recommend the Asus Eee PC 1000H. It's small and light - 1.45kg - but sturdy. Not bad specs either - 1GB ram, 80 GB HDD, Atom processor, wifi and bluetooth, up to seven hours of battery life, but note there is no optical drive. Retro games - anything pre 2004 or so - should play on it reasonably well.
It comes with XP but you can put Linux on it. I know several distros including Ubuntu have been customised to work with the Eee's hardware. There's also a flourishing forum for help and support too. Highly recommended. Since getting this I've hardly touched my large and powerful VAIO!
Holly - 7years
Amber- 3 years