Ouch, a 250 watt PSU really limits your choices. What resolution do you plan on playing at?
An HD 6450 is actually a decent card for quiet, power-efficient HTPC duty, but it does indeed fall short for gaming. Here are some other options:
http://www.newegg.com/Product/Produc...-380-_-Product
^^A Radeon HD 5570 with a passive cooler. $59.99 list price, $49.99 after mail-in rebate. Thanks to the passive cooler this is probably the quietest and most power-efficient, but the graphics chip itself is not very powerful. (better than the 6450 though)
http://www.newegg.com/Product/Produc...-374-_-Product
^^A Radeon HD 6570 with a passive cooler. Again, quiet and power efficient. Packs a bit more of a punch than the 5570, but it is also significantly more expensive. ($74.99)
http://www.newegg.com/Product/Produc...-871-_-Product
^^ Radeon HD 5670, actively cooled. More powerful than the 5570 and a bit better than the 6570, but also noisier and more power-hungry. Less expensive than the 6570 though -- $69.99 list price, $59.99 after mail-in rebate.
http://www.newegg.com/Product/Produc...-542-_-Product
^^Radeon HD 6670, actively cooled. This is probably the most powerful card you can get to work on your PSU. Same noise level as the 5670. $83.99 list price, $73.99 after mail-in rebate. This particular card comes with a free double-lifetime warranty -- meaning if you resell this card to someone the warranty carries over to them.
Edit: The above card has only GDDR3 memory, making it slower in some ways than the 5670 and not much better than the 6570. Here is a proper 6670 with GDDR5 memory ($96.99):
http://www.newegg.com/Product/Produc...-935-_-Product