I got my mother a Dell inspiron ONE 2310. (Just the basic model, a pentium and Intel HD graphics)
It easily handles watching videos, playing DVDs, listening to music, surfing the net and typing up documents.
I haven't tried any proper games on but its not a very high spec' so I don't expect much.
The base model didn't have a TV decoder but you can always stick in a USB device.
Wireless keyboard and mouse are comfortable, accurate and responsive, no loss of connection at all.
Then theres the touch screen. Wonderfull.
The default screen font was too small e.g. when trying to select individual menu items from a list of words. Even on a 23" (full HD) screen!
To make Windows 7 a bit easier to use, I changed the font size to 150%. As well as more readable text this also gives you bigger areas for normal sized human fingers to fit.
IE9 is fully touch ready, other browsers not so integrated. Windows 7 itself could also have more touch features throughout.
Microsoft are working on that but of course they will call it windows 8 and will be charging for it!
So go for a higher spec' with discrete graphics card but expect to may more than you would for the equivalent desktop box and monitor.
I was at the Microsoft Store a couple weeks ago, and I came across an HP TouchSmart 610 Quad Series customizable PC. I played with it quite a bit and it was really fun to use. It had a 23" screen, and the screen was not overly touch sensitive; the touch sensitivity was just right, feels just like the touchscreens I use at work. I didn't have to press too lightly or too hard for my touch to go through. It had a 2nd generation Intel i7 quad-core processor, powered with a choice of several powerful graphics cards. The wireless keyboard and mouse that were with the PC were great as well. It's an All In One PC that I'd love to own, and I would recommend checking it out if you are interested in All in One PCs.