Assuming you're talking about displaying, and maybe very simple editing of photos (like removing red eye), and the games are along the lines of simple educational games, pretty much anything will do. I know the other person meant well, but they vastly overstated what you need. Though that may be what's getting to be entry level these days. Ever since I moved to using consoles for gaming, I haven't had the need to upgrade my system nearly as much, so tend to lose track.
I will say that I'm a big fan of building your own system. With systems from Dell, Gateway, etc, particularly low end models, they are going to cut every possible corner in making the system to keep costs as low as possible. This may mean they're using dozens of different suppliers for different batches of systems, all depending on who gives the lowest quote at the time. The thing to remember about the lowest bidder, is that they still want to make a profit off of the transaction, so what exactly are they doing that they can offer such a low price? It could be anything from selling parts that were supposed to be disposed of because they didn't meet quality control standards, to using virtual slave labor.
If you build yourself, you spend a bit more, and it's more work, but you have very strict control over the quality of the parts going in. Ultimately, this leads to a much more problem free system. And if you don't think you're up to the task of putting everything together, or just worried about a bunch of small parts laying about with small children in the house, there are places that will let you pick out components and then assemble a system from those parts. Those are both actual examples of things that have gone on, if not still going on.
Monarch Computer is one such place with a good reputation. I'd strongly suggest taking it one part at a time, and then going to hardware review sites like Tom's Hardware to research each and every part offered in each category. It will be time consuming and laborious, but the result will be a system that is likely to last far longer than any el cheapo system you get from Dell, HP, Gateway, etc, and be far less problematic.
But, if you would rather just have something now, and take your chances... Pretty much any system you can buy will be suitable. I wouldn't worry about the CPU speed so much as making sure you have at least 512MB of RAM. Whether the system comes with XP or Vista, you don't want to be dealing with anything less than 512MB of RAM.