I wouldn't recommend anything less than a 350w PSU for the Radeon HD 7770. The closer the PSU is working near it's maximum capacity, the shorter it's lifespan will become. The total wattage is a general number, what's more important is the amount of amps provided on the +12v rails since most of the power the PC draws is from the +12v rails.
You can be the following Corsair 430w PSU for $25 after rebate + $6 shipping.
http://www.newegg.ca/Product/Product.aspx?Item=N82E16817139026
There is also the Corsair 500w PSU for $40 after rebate + $6 shipping
http://www.newegg.ca/Product/Product.aspx?Item=N82E16817139027
Naturally opting for the 500w Corsair will give you extra headroom if you decide to upgrade to a more powerful graphics card in the future which also generally means higher power consumption.