I'm building my first computer soon and I wanted to know whether getting the 1GB 5770 would make a noticeable difference in gameplay over the 512mb version. I've only got a 19" 1440 x 900 screen.
Or should I get the 4870 1GB?
Or is there a card around the same price that would be better suited to gaming, and which wont need to be upgraded straight away.
I've got upto about £120 ($USD185) for a graphics card.
You're fine for a 5770 512MB. However, if you're interested in overclocking, most AIBs will put the non-reference cooler on the 1GB version. It's a worthy envestment for a 1GB as you'll need it if you upgrade your monitor some.
The 4870 and 4890 are great, but no DX11 support for the latest games. At your current resolution, the 512mb version is fine, but if you are going to upgrade to 1680x1050 or higher in the future, you'll want the 1gb version. I would suggest the 5770 over the others just because of DX11, and pricewise, the others are going up and getting harder to find.
I would get the 1GB card simply because newer games will show a benefit with the extra memory, even at 1440x900. Granted it's generally not much, but as games use more and more vRam the card will last you a little longer if it has more to work with . As others have said, get the 5770 over the 4870 if you can afford it.