I have a HD7770 and am happy with it. I got it about a year ago for 90.00 before all the price cuts, so it was a good price at that time. If I were buying now though, I would try to get the 7790 or even a 7850. As long as supply lasts, the price is incredibly good on those cards right now.
I would agree with Nickname though, try to get at least the unlocked x4 750k or even the 6300. Having a bit more cpu power will perhaps mean you can go a bit longer without upgrading.
So I would advise trying to save up a bit more and go for the x4 750k and 7790.
On new egg the cheapest 7790 is 20 dollars more that the cheapest 7770. Definitely seems worth it. And surprisingly, the 750k and 740 are listed at the same price (???).
Only other thing is 750k has 100w tdp vs 65w for the 740, so it might require a slightly better motherboard, especially if you want to overclock, but I dont know enough about motherboards, especially AMD, to make suggestions.