Given that Intel's integrated graphics pretty much kicks AMD's counterpart by far now days I'd say stick with it since your parents probably wont need "gaming" performance (AMD performs slightly better in games but its still useless compared to dedicated). If needed you can add a video card in the future without any hassle.
What might be of interest are these two articles
I would really recommend you NOT to get one of the cheapest monitors around which by the way are TN panels. They perform very poor unless you sit in the exact "correct" angle and you have noticeable variations of brightness so if you hate your parents its a good buy.
Since you haven't specified a budget I've taken in consideration that they plan to have it for a while and have good components so you wont run into issues in the future both performance wise and upgradable.
Comparing these two computers (I'm not including keyboard, mouse and monitor) there's a ~100Â£ difference in price (added the same ODD as I used). What you get is a ~10-20% faster CPU, better video acceleration, better (faster and more efficient) chipset and LAN (network card), 500Gb larger HDD (the difference is so small it would be unwise not to go for 1TB), quieter (since the Intel system will use less power) and better compatibility (having drivers in mind). If you don't find it useful go for the cheaper system.
Getting a PSU separately is usually better but since you're aiming for a rather "low-end" machine cases that comes with a PSU will do fine.