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sankarshan, in answer to your question "What is the first-most criteria i should consider for purchasing graphics card?", I would simply respond that you're generally trying to get the most powerful graphics card in your price range. If you'd like a general idea of hierarchy of graphics cards, then this is good resource:
Best Graphics Cards For The Money Hierarchy list:
http://www.tomshardware.com/reviews/gaming-graphics-card-review,3107-7.html
The least powerful cards are on the bottom and they get progressively more powerful, as you work your way up on the list. The left column contains Nvidia cards and the right AMD. Ideally, it would be great if you could get a GTX 750 or 750 Ti (Titanium) but those are at least twice your budget, if not more. Also, your AMD sempron will most likely be a bottleneck regardless. I don't say that to be offensive but instead to be complete transparent in my thinking in reference to your computer build.
Addendum:
I actually used to have a very similar computer. I previously had a AMD Athlon 3500+ but mine was a single core CPU. I'm reasonably sure that your motherboard only has a first generation PCIe Express 16x slot; current computers have PCIe version 3.0. If my assumption is correct then your computer will only support a graphics card with only one generation newer than yours, PCIe 2.0. Anyone else reading this message thread, please feel free to correct what I'm stating as I'm not 100% on this point. I don't think this is going to be much of a problem, because the low budget will probably only allow buying a card of that generation anyway.
Page I used to see motherboard specs:
http://www.gigabyte.com/products/product-page.aspx?pid=3645#ov