There are several GTS 250s (at 512 mb) within your price range. Just checked newegg myself. I'm sure some other sites will get you a 1GB 250 for around $120. That would be your best bet given your budget.
Moving below that price range a tad, you could also go for a GeForce 9800 GT or a Radeon 4830.
For the price you want to pay, it'll be hard to find a decent card with the things you want.
Wait and save up some more money. The cards in that price range are quite lacking for the resolution you are talking about. Saving up for an HD5770 would be my recommendation.
Ok. I also wanted to know which would be better - a card with 1gb memory or a 512mb card which is faster than the other card.
For 1920x1080 a 1gb card is better.
ok i decided on HD 4770 or HD 5750. I think they cost around the same near my place (India). so which do you guys think is better?
The HD5750 is more powerful, DX11 compatible and supports 3 monitors so that's an easy choice if they are the same price.