I also looked at HD 6670 which is quite cheaper but some sites mentioned that HD5770 is much much better than it?
Yea the HD5770 is a more powerful card.
Here's a suggestion for your build (Prices are approx)
Phenom II x4 965 - 7k
Asus m5a88-M - 5.5k
6gb(2x3) 1333mhz GSkill/Corsair/Kingston Value ram - 2.5k
ATI HD 6770 - 6.5k
Seasonic S12II 620 - 4.5k
Lancool PC-K58W - 4k
Total - 30k
Leaves the rest for your monitor & speakers etc.