I got the same CPU and Ram config
and was running a GeForce 8800 GT with a 22" (1680x1050)
never had really probs with drivers or games.
(Now I placed another 8500 GT next to the 8800 GT and use SoftTH for triple monitor gaming :-) )
But to your original question.
HD is better the (really outdated) X designations
and 58xx (DX11) is better the 4xxx (DX10 / 10.1) series ;-)
Some more info:
My plan atm is to switch to ATI for the first time (in almost 20 years)
as the new HD 58XX cards can do 3 (up to 6) screens alone (with 2xDVI and 1DisplayPort)
and the eyefinity technology.
Unfortunately the card I want is hard to get atm and way to expensive
and Monitors with Displayports are also too expensive atm
and an adapter to use DVI to DP is also not really available
So I stay with SothTH for the next half year I bet.
So what choices you got?
The best cheapest Radeon for normal use is the
Radeon HD 4890 (but it can only use Direct X 10.1 which is more or less useless as all new games switched from DX9 to DX11) and has no eyefinity option
So I would go for a 5xxx series (As they can do Direct X 11 and eyefinity)
If you plan to only use 2 Monitors at the same time
Then the 5770 is good enough or you wait for the coming 5830 versions
which should be better in price
If you want to use more then 2 screens I would go for at least an 5850 (<-- my plan)
and if money is no problem an 5870 ;-)
So the question is what you want to do.
Double Screens
Triple Screens
Gaming
Just Gfx stuff
etc.
If you really want to also play with the PC I would never ever use a passively cooled card.
They are good enough to run my mediaportal for watching HD movies etc. but not for gaming.
The new 5xxx series cards have a very low power consumption, have really quiet fans and
are quick enough and can do Dx11.
So after checking all the pros and cons I decided to get myself a 5850 card (when the price is back down to 200 euros) instead of Nvidia.
And I usually always bought , installed , sold to customers Nvidia. So that means something ;-)
Bad thing atm:
ATI got massive delivery problems atm because TSMC (Taiwan Semiconductor Manufactoring)
got problems with gaining (rumours say it's only 50% to 60%) not enough good 40nm chips out of their silicon wafer atm. So all are running out on new 40 nm GPU chips.
So the price here jumped from 200 euros at christmas last year for an 5850 card up to 280 to 300 Euros
for the same cards. (but they are not often deliverable here atm anyway -first companies like DELL etc get cards then the enduser)
I would wait a bit to get a new ati card as the price will go down drastically in the next 2 or 3 months.
When they get the problems with the GPUs fixed.
And last but not least I would advise you to look for a Radeon HD 5830 then if you will stay with your 2 (also new 1980x1080) monitor setup.
Hope that helps you somehow

Btw since I saw this review about the eyefinity stuff I knew I wanted it :-)
http://hardocp.com/article/2009/09/28/amds_ati_eyefinity_technology_review(vid is a bit down middle of the website)
even if I use SoftTH atm I will not miss 3 sceens for some games especially LFS