Hi Emma @Emma McManus , I'm Lee and welcome to FG! Phil @phil bottle and La @RenFengge above has been pretty good so far and I wouldn't be disagreeing with him much in terms of questions. I assume you are looking for a ready made PC and not to be made by yourself? I was assured by the rest of the FG people here that these days there isn't as much difference to cost as it used to be back in the day so for less hassle i'll go with the ready made.
The PC Tower (with all the bits to make it work in it)
Monitor
Keyboard
Mouse
Operating System (like Windows 7, etc)
Chair
Desk
I apologies in advance if this is teaching you to suck eggs but you never know what people have thought about and allowed room in their budget for these things. If you're buying a ready made PC, they'll usually come with parts 1-5 (although 5 can be missing in some bundles so beware).
Those games won't require a huge amount of 'top spec' for them to work, however as he is nearly 10, I would imagine he'll be wanting to be play first person shooters before you know it and that when you need a little more oomph.
Would it help if we found a few links on some low budget, on budget, and over budget bundles on the internet to help your selection? We could probably help with all the rest too if needed as theres been previous topics on what chairs and desks people want these days too.
@Greboth @Diddums @Tar-Eruntalion @Spacedeck @BO7H B4RRELS @The3rdWalker - just tagging a few core PC players if they can add anything to help with what you need!