I have a Radeon 3200 HD card (integrated). I have my 32" HDTV running 1080p and my other monitor running 1680x1050. One is HDMI, the other is VGA. I run videos, Aero, etc perfectly fine. I have some issues with skipping, but that is a CPU issue (it's been happening for weeks while this setup has only been running for a week). The 7800GTX is a pretty decent card, as far as I can remember offhand, although I'm not positive. If my integrated card could handle what I have running, I'm sure the 7800 can. Dont take my word for it though.
As for a choice for a new monitor, I have to go against Larry. Samsung is a really good brand... Dell is pretty good too, and usually cheaper, but Samsung is known for quality. For myself, I would choose Samsung without blinking. However, it is a matter of preference. Look up reviews for the two and see which one is better.
As another option, I have a Sharp 32" 1080p HDTV set up as my primary monitor - It's the most incredible setup I have and I can easily buy a blu-ray drive and run HD content easily. I have a Logitech Dinovo Edge keyboard, so my setup works great. Something to consider anyways.
Be nice to nerds.... chances are you will end up working for one
ASUS M3A78-EMH HDMI
AMD Athlon X2 6000+ o/c'd at 3.2GHz
4GB (2x2GB) OCZ RAM
Integrated Radeon HD 3200 (HDMI out)
500GB SATA/360GB IDE HDD's
32" Sharp 1080p Monitor/TV
Vista RTM/Vista SP2 Beta/7 6801