1600x1200... OK, I understand now. You have a 1600x1200 CRT monitor. That is a good resolution for gaming, although the old 4:3 squarish display must be like wearing blinders in a game designed for wide screen. I would get a faster card and run Windows and your games at that resolution. Your 2.8GHZ C2D will give you good frame rates at that resolution with a faster card.
About the GTX 550ti...
It is in the same tier as the HD 6770 according to the hierarchy chart I linked you to. But it is a major upgrade to the HD 6750 w/DDR3 VRAM. Either the 550ti or the 6770 would be adequate for high-ish settings at 1600x1200 resolution in most games.
Now, on to the monitor question...
The only thing wrong with gaming on a monitor with a 4:3 aspect ratio, is that you lose the beauty and extra visual real estate available with a wide-screen (16:10, 16x9) LCD/LED monitor. And yes, your friends are correct; gaming on a higher resolution wide screen monitor makes for a better looking game environment. You will feel like you took off the blinders. You will see more area of the game with your peripheral vision. And all of today's games are written for the wide screen displays. But keep in mind, the higher the resolution, the more powerful the gfx card needs to be to maintain fast, smooth frame rates.
If you stay with your 1600x1200 CRT monitor and run games at that resolution, don't waste your money on anything less than the 550ti/6770. Maybe go even a step above. But if you continue to play at lower resolution than that, those cards will be more than enough.